I have been trying to read up on 32-bit and 64-bit processors (http://en.wikipedia.org/wiki/32-bit_processing). My understanding is that a 32-bit processor (like x86) has registers 32-bits wide. I'm not sure what that means. So it has special "memory spaces" that can store integer values up to 2^32?
I don't want to sound stupid, but I have no idea about processors. I'm assuming 64-bits is, in general, better than 32-bits. Although my computer now (one year old, Win 7, Intel Atom) has a 32-bit processor.
32bit processors can address a memory bank with 32 bit address with. So you can have 2^32 memory cells and therefore a limited amount of addressable memory (~ 4GB). Even when you add another memory bank to your machine it can not be addressed. 64bit machines therefore can address up to 2^64 memory cells.
32-bit and 64-bit are basically the registers size, register the fastest type of memory and is closest to the CPU. A 64-bit processor can store more data for addressing and transmission than a 32-bit register but there are other factors also on the basis of the speed of the processor is measured such as the number of cores, cache memory, architecture etc.
Reference: Difference between 32-bit processor and 64-bit processor