<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>0201 - Disclosure - Nature of Business and Organization</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2011 - 3/31/2011
USD ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>Jan-01-2011_Mar-31-2011</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001106942</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2011-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2011-03-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><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></UnitProperty><UnitProperty><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></UnitProperty><UnitProperty><UnitID>USDEPS</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></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="3 Months Ended" /><Label Id="2" Label="Mar. 31, 2011" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_GeneralPoliciesAbstract</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><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Nature of Business and Organization [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</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><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 1 - us-gaap:NatureOfOperations--&gt;
   &lt;div align="left" style="margin-left: 0%"&gt;&lt;!-- XBRL,ns --&gt;
   &lt;!-- xbrl,nx --&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent"&gt;
   &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;&lt;/div&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent"&gt;
   &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;/font&gt;&lt;/b&gt;
   &lt;/div&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; text-indent: 0%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
   &lt;b&gt;
   &lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;&lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
   &lt;i&gt;
   &lt;/i&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 12pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;table width="100%" border="0" cellpadding="0" cellspacing="0" style="font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent; text-align: left"&gt;
   &lt;tr&gt;
       &lt;td width="3%"&gt;&lt;/td&gt;
       &lt;td width="97%"&gt;&lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="top"&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;1.&amp;#160;&amp;#160;&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;Nature of
       Business and Organization&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;/table&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 4%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       Blackboard Inc. (the &amp;#8220;Company&amp;#8221;) is a leading provider
       of enterprise software applications and related services to the
       education industry. The Company&amp;#8217;s clients include colleges,
       universities, schools and other education providers, textbook
       publishers and student-focused merchants who serve these
       education providers and their students, and corporate and
       government clients. The Company&amp;#8217;s software applications are
       delivered in six product lines: &lt;i&gt;Blackboard
       Learn&lt;sup style="font-size: 85%; vertical-align: top"&gt;&lt;font style="font-variant: small-caps"&gt;tm&lt;/font&gt;&lt;/sup&gt;&lt;/i&gt;;
       &lt;i&gt;Blackboard
       Transact&lt;sup style="font-size: 85%; vertical-align: top"&gt;&lt;font style="font-variant: small-caps"&gt;tm&lt;/font&gt;&lt;/sup&gt;&lt;/i&gt;;
       &lt;i&gt;Blackboard
       Connect&lt;sup style="font-size: 85%; vertical-align: top"&gt;&lt;font style="font-variant: small-caps"&gt;tm&lt;/font&gt;&lt;/sup&gt;&lt;/i&gt;;
       &lt;i&gt;Blackboard
       Mobile&lt;sup style="font-size: 85%; vertical-align: top"&gt;&lt;font style="font-variant: small-caps"&gt;tm&lt;/font&gt;&lt;/sup&gt;&lt;/i&gt;;
       &lt;i&gt;Blackboard
       Collaborate&lt;sup style="font-size: 85%; vertical-align: top"&gt;&lt;font style="font-variant: small-caps"&gt;tm&lt;/font&gt;&lt;/sup&gt;&lt;/i&gt;;
       and &lt;i&gt;Blackboard
       Analytics&lt;sup style="font-size: 85%; vertical-align: top"&gt;&lt;font style="font-variant: small-caps"&gt;tm&lt;/font&gt;&lt;/sup&gt;&lt;/i&gt;.
       The Company also offers application hosting for clients who
       prefer to outsource the management of their &lt;i&gt;Blackboard Learn
       &lt;/i&gt;systems, and the &lt;i&gt;Blackboard Student
       Services&lt;sup style="font-size: 85%; vertical-align: top"&gt;SM&lt;/sup&gt;&lt;/i&gt;
       offering, which includes student lifecycle management and IT
       support services. In addition, the Company offers a variety of
       professional services, including strategic consulting, project
       management, custom application development and training.
   &lt;/div&gt;
   &lt;/div&gt;
</NonNumbericText><NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</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><IsEPS>false</IsEPS><Label>Nature of Business and Organization</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Nature of Business and Organization</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
