Layman answer from Google:
Think of your computer as a series of tubes that can either be 32 or 64 bits wide. When you have the smaller 32-bit size, there is more potential for bottlenecks to occur. Bottlenecks slow down your system because one process has to wait for another to finish before it can begin. But if you want to have 64-bit wide tubes, your computer needs to be thinking in 64-bit so your software and hardware all need to support 64-bit.
On a 32-bit operating system, you are restricted to a maximum of 4 gigabytes of RAM. On a 64-bit operating system, you really do not have a limit.
Something like that!!!