As far as 64-bit OS's are concerned, the bit size, among other more important details, is an indication of how large the maximum RAM a computer can have/use without an address extension.
32 bit computers can have a maximum of 2^32 bits, or 4 GB, of RAM. We have gotten to the point where 4 GB is easy to use and get - this is where the 64-bit OS comes into play.
A 64 bit OS can use up to 2^64 bits of RAM, or 16 exabytes of ram (roughly 17.2 billion GB). Excepting the usefulness of calculating with very large numbers efficiently, we won't need more than 64-bits until we can use over 16 exabytes of RAM.