64 bit OS allows you to use more then 4gb of ram... the acutal ammount that will be usable under 32 bit OS will be a bit less then 4gb.
It also allows you to run 64bit applications, which while they are more efficeint then 32 bit apps, the ammount of them on the market is still woefully small, and mostly limited to proffesional grade softwares such as adobe suite, etc...
MOST of your 32 bit applications will run under 64bit OS. Drivers INTENDED for 32bit, and applications that interact heavily with the OS (for example your anti-virus, or a CD/DVD emulator program) Will most likely not work - you will need to obtain a 64 bit version.
Other Programs and games should all work since they interact with your drivers (which are 64bit compatible) and not with windows directly - this is the primary reason that Direct X exists, for the games at least.