The official Microsoft explanation states that “The terms 32-bit and 64-bit refer to the way a computer’s processor (also called a CPU), handles information. The 64-bit version of Windows handles large amounts of random access memory (RAM) more effectively than a 32-bit system.” (http://windowshelp.microsoft.com)
Essentially, what this means is that a 32 bit operating system works better when you have a small amount of memory (RAM) and 64 bit operating systems work better with large amounts of RAM. So, what is a large amount of RAM? The answer to this question changes every year. At the time of this writing, 4GB or more is considered a large amount of RAM. Conveniently, this is also the realistic boundary at which you will choose one or the other architecture. If your computer has at least 4GB of RAM, choose a 64 bit OS. Any less and you should stick with 32 bit.
Here are some other FAQs related to 32 bit vs 64 bit computing:
Here is another link to a Microsoft site which compares the different Vista operating systems. This information and advice should stay relevant through the Windows 7 release – due October 22nd 2009. http://www.microsoft.com/windows/windows-vista/compare-editions/64-bit.aspx