﻿<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Description of Business</ReportName>
  <ReportLongName>1010 - Disclosure - Description of Business</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="9 Months Ended" />
        <Label Id="2" Label="Sep. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDPerShare</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Description of Business</Label>
      <Level>0</Level>
      <ElementName>amag_DescriptionOfBusinessDisclosureAbstract</ElementName>
      <ElementPrefix>amag</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Description of Business</Label>
      <Level>1</Level>
      <ElementName>us-gaap_NatureOfOperations</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>terselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;table style="font-size:10pt; font-family:'Times New Roman',times,serif;"&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in"&gt;&lt;b&gt;&lt;font style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;A.&lt;/font&gt;&lt;/b&gt;&lt;b&gt;&lt;font style="FONT-WEIGHT: bold; FONT-SIZE: 3pt" size="1"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/font&gt;&lt;/b&gt; &lt;b&gt;&lt;font style="FONT-WEIGHT: bold; FONT-SIZE: 10pt" size="2"&gt;Description of Business&lt;/font&gt;&lt;/b&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;&amp;nbsp;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;AMAG Pharmaceuticals,&amp;nbsp;Inc., a Delaware corporation, was founded in 1981. We are a biopharmaceutical company focused on the development and commercialization of a therapeutic iron compound to treat iron deficiency anemia, or IDA. Our principal source of revenue is from the sale of Feraheme&lt;/font&gt;&lt;font style="FONT-SIZE: 6.5pt; POSITION: relative; TOP: -3pt" size="1"&gt;&amp;#174; &lt;/font&gt;&lt;font style="FONT-SIZE: 10pt" size="2"&gt;(ferumoxytol) Injection for intravenous, or IV, use, which was approved for marketing in the U.S. in June&amp;nbsp;2009 by the U.S. Food and Drug Administration, or the FDA, for use as an IV iron replacement therapy for the treatment of IDA in adult patients with chronic kidney disease, or CKD. We market and sell &lt;i&gt;Feraheme&lt;/i&gt; in the U.S. through our own commercial organization and began shipping &lt;i&gt;Feraheme&lt;/i&gt; to our customers in July&amp;nbsp;2009.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;&amp;nbsp;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;i&gt;&lt;font style="FONT-SIZE: 10pt; FONT-STYLE: italic; FONT-FAMILY: Times New Roman" size="2"&gt;GastroMARK,&lt;/font&gt;&lt;/i&gt;&lt;font style="FONT-SIZE: 10pt" size="2"&gt; our oral contrast agent used for delineating the bowel in magnetic resonance imaging, is approved and marketed in the U.S., Europe and other countries, through our marketing partners.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;&amp;nbsp;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;We are subject to risks common to companies in the pharmaceutical industry including, but not limited to, our sole dependence on the success of &lt;i&gt;Feraheme&lt;/i&gt;, the potential development of significant safety or drug interaction problems with respect to &lt;i&gt;Feraheme &lt;/i&gt;and the need for potential changes to the &lt;i&gt;Feraheme&lt;/i&gt;  package insert related thereto, competition in our industry, uncertainties regarding market acceptance of &lt;i&gt;Feraheme&lt;/i&gt;, uncertainties related to patient insurance coverage, coding and third-party reimbursement for &lt;i&gt;Feraheme&lt;/i&gt;, our limited experience commercializing and distributing a pharmaceutical product, our reliance on our partners to commercialize &lt;i&gt;Feraheme&lt;/i&gt; in certain territories outside of the U.S., our potential inability to operate our manufacturing facility in compliance with current good manufacturing practices, our potential inability to obtain raw materials and manufacture sufficient quantities of &lt;i&gt;Feraheme&lt;/i&gt;, the potential fluctuation of our operating results, potential differences between actual future results and the estimates or assumptions used by us in preparation of our condensed consolidated financial statements, the volatility of our stock price, our potential inability to become profitable in the future, our potential inability to obtain additional financing, if necessary, on acceptable terms, our potential inadvertent failure to comply with reporting and payment obligations under government pricing programs, our potential inadvertent failure to comply with the regulations of the FDA or other federal, state or foreign government agencies, uncertainty of the regulatory approval process for our other &lt;i&gt;Feraheme &lt;/i&gt;indications, for any indications outside of the U.S. or for potential second source manufacturing facilities, uncertainty of the results of our clinical trials, our dependence on key personnel, and uncertainties related to the protection of proprietary technology, potential product liability, potential legislative and regulatory changes, and potential costs and liabilities associated with pending or future litigation.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;&amp;nbsp;&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt; TEXT-INDENT: 0.25in"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: Times New Roman" size="2"&gt;Throughout this Quarterly Report on Form&amp;nbsp;10-Q, AMAG Pharmaceuticals,&amp;nbsp;Inc. and our consolidated subsidiaries are collectively referred to as &amp;#147;the Company,&amp;#148; &amp;#147;we,&amp;#148; &amp;#147;us,&amp;#148; or &amp;#147;our.&amp;#148;&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
</NonNumbericText>
          <NonNumericTextHeader>A.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Description of Business
&amp;nbsp;
AMAG Pharmaceuticals,&amp;nbsp;Inc., a Delaware corporation,</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>Describes the nature of an entity's business, the major products or services it sells or provides and its principal markets, including the locations of those markets. If the entity operates in more than one business, the disclosure also indicates the relative importance of its operations in each business and the basis for the determination (for example, assets, revenues, or earnings). Disclosures about the nature of operations need not be quantified; relative importance could be conveyed by use of terms such as "predominately", "about equally", or "major and other". This element is also referred to as "Business Description".</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Statement of Position (SOP)
 -Number 94-6
 -Paragraph 10

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
