Well, I'm definately not an expert, but one small comparison could be with registers.
For example, in assembly, there exist a restricted number of variables.
In 16 bits assembly, the registers would be:
CS, DS, ES, SS
AX, BX, CX, EX
IP, SP, BP
SI, DI
Note that all registers with a 'X' as the suffixe consist of two "sub" registers. ex: AX = AL + AH.
Basically, 32 bits brings in more registers and so does 64 bits. Why would we want more registers? It means we can keep more local information stored in those registers (vital information) and have less access to the memory. Therefore, memory access is reduced thus speeding the process.
Also, I believe the size of an integer, for instance, passes from 32 bits to 64 bits. Hence, more information can be stored in a single occurrence.
That's probably as far as I know concerning the 64 bits architecture. As I said, I'm definately
not an expert.
Try searching in wikipedia or google or if you're looking for something heavier, try looking at
http://computer.howstuffworks.com/microprocessor6.htm
Great website if you're wondering
how stuff works
P.S.: If I posted any errors, please do rectify the errors!