“Power BI” is an umbrella name for a lot of products, which I explain at Power BI first impressions (also I have a video at Power BI for Office 365 video). Each of these products have different requirements:
Power Query: Is an Excel add-in that you download and install. It requires Excel 2010 SP1 or Excel 2013. Works for 32-bit or 64-bit, but 64-bit is highly recommended.
Power View: Included with Excel 2013, you just need to enable it. Works for 32-bit or 64-bit, but 64-bit is highly recommended. There is not an add-in version for Excel 2010. Can also be used through SharePoint: run the SQL Server 2012 install (Business Intelligence edition or Enterprise Edition) and on the Feature Selection page choose “Reporting Services Add-in for SharePoint Products”. Requires Microsoft SharePoint Server 2010 Enterprise Edition, Reporting Services 2012 in SharePoint integrated mode and Analysis Services.
Power Map: Is an Excel add-in that you download and install. It requires Excel 2013 – Excel 2010 is not supported. Works for 32-bit or 64-bit, but 64-bit is highly recommended.
Power BI Sites: If you are accepted to the Power BI for Office 365 preview you will be given a SharePoint Online account. On this SharePoint Online site you will be able to add a “Power BI sites” application that allows you to share workbooks and use other BI features.
Data Management Gateway: This is a client agent (download) that enables cloud access for on-premises data sources on your server and exposes data from these on-premises data sources as OData feeds for corporate-wide access via Power Query. Works with Windows 7, Windows 8, Windows Server 2008 R2, and Windows Server 2012.
Power BI for mobile: An app you download. Works for Windows 8/RT devices.
Power BI Q&A: Included with Power BI SItes.