Judi, here is an analogy for you... imagine you had a highway with 32 lanes... you could therfore send 32 cars (on per lane) down the highway simultaneously (side-by-side). In computer terms, this is the same concepts as a 32bit system, except it is not car but data (a 1 or a 0).

A 64bit system is exactly the same concept, just with 64 lanes on the highway. Also as you were totally correct, the more lanes you have the more memory you can access (memory addresses)... it's gets a bit nerdier on from here!