If you go to File -> Help within Outlook 2010, in the right most pane, it will show you the version of Outlook, ex 14.0.6106.5005 (32-bit). If it says (64-bit), then your computer is running Windows 64 and Outlook 64-bit. Outlook 2010 32-bit is supported, 64-bit is not.
64-Bit Outlook would take advantage of the 64-bit nature of the operating system, and allow for larger memory access, as well as other features. However, 32 bit is the more traditional version, for which most software was originally written for that's more than 5 years old. Seems software companies are just now starting to roll out 64-bit compatible software.