Basically there are four editions:
Home Basic - This is Windows XP with a better skin, higher system requirements and lower performance. Highly NOT recommended.
Home Premium - This is the version most people would and should opt for. It has Aero and Windows Media Center, among other things.
Business - As the name says, it is meant for businesses.
Ultimate - The full-fledged and costliest version of Windows Vista. It is Home Premium and Business rolled into one. Basically, it is Home Premium with a boatload of other features that you cannot even spell and will likely never use. Microsoft figured that some people would buy it because the name sounds impressive and they would make a few extra bucks.
All these editions have 32 and 64 bit versions and can be had for a lower price if you are upgrading from a legitimate version of Windows XP.