Yes, a 64-bit CPU and OS can address a huge amount of RAM (16 exabytes versus only 4 GB!), and in addition, for apps that are coded for 64-bit, they can perform some operations faster. See
http://en.wikipedia.org/wiki/64-bit. Also, there was a demo by the Steve on I believe iPhoto or Photoshop or something of 32-bit versus 64-bit. For large libraries of photos, or for an extremely large photo, there is a huge performance increase with 64-bit.
But for general use, most people won't notice any improvement.