For most consumers that is the major difference.
If you buy the retail or upgrade version it comes w/ both 32 bit & 64 bit on same DVD. You can install either.
If you are buying OEM version you need to pick either 32 bit or 64 bit. What processor does your computer have? If it doesn't support 64bit then you have to go 32bit. Otherwise IMHO 64bit is better choice because you may want to expand or upgrade the machine in the future.
If you are not sure about what CPU you have here is a good free tool:
http://www.cpuid.com/cpuz.phpYou can install it but I just grab the zipped version, unzip to a folder, double click to run, and you can just delete folder when you are done.
CPU tab will shows all the info about your CPU.
In the box labeled "Instructions" it shows the instruction sets supported by the CPU. x64 is what you are looking for. x64 is support for 64bit instructions.