For cpus, like when you talk about a 16-, 32-, or 64-bit cpu, its supposed to mean that the cpu can manipulate data values of that precision atomically.
So on a 64-bit cpu, you can do math with 64-bit numbers with no performance hit as you would have on a 32-bit cpu, and you can have more available system memory because now your memory addresses can be 64-bits long rather than 32-bits long.
x86-64 itself specifies that more registers will be available as well.
So yea, I guess that also means that the registers are 64-bits long rather than 32- or 16-.