Your CPU is 64-bit capable. You don't *need* 64-bit to run Windows 7, but if your CPU is 64-bit capable you might as well install the 64-bit flavor since it will enable you to use more than 4 GB of RAM effectively.
@DrkSide - Many of the Prescott P4s did not support 64-bit. For a while, Intel was intentionally disabling this feature on some models to artificially segment their product line.
(Edited - I originally posted that there were Core 2s without 64-bit, but I now believe this was incorrect. There were definitely 32-bit only Prescotts, I had one at work until just a couple of years ago.)
If the world isn't making sense to you, you're either drinking too much or not drinking enough.