The "bit", refers to the width of the register. A 64-bit register can hold more data than a 32-bit register, and, subsequently, which in turn holds more than 16-bit and 8-bit registers. The more ample the space in the CPU’s register system, the more it can handle—especially in terms of using system memory efficiently, and so run faster.
One important factor which came up when programmers began to make more memory intensive applications (Apps), was that a computer with 8 GB of RAM was considerably more responsive than one with 4 GB of RAM. 32-bit PCs were limited to 4 GB of RAM. 64Bit were not.
There are more technical considerations, but for the avergae user, that is enough to know.