The difference between Windows XP 32-bit and Windows XP 64-bit is in the amount of RAM that the OS will support. A 32-bit OS (XP or Vista) will only support up to 4GB of RAM (tho usually XP 32-bit will only recognize about 3.25GB of RAM.) A 64-bit OS (XP or Vista) will (theoretically) take up to 16 Exabytes of RAM (EB being the next step beyond TB, which is the next step beyond GB.) Realistically, most people use a 64-bit OS to use 4-16GB of RAM.
You should be able to tell if your XP is 64-bit or not by right clicking on "My Computer," and selecting "Properties." This will give you your system information, and it should say right there.
As a side note - Microsoft only made a 64-bit version of Windows XP Pro - not Home. So, if you've got XP Home, then you've got a 32-bit OS.
Hope that helps!