CPU bitness refers to the number of bits on which a CPU operates on at a time. Typically, phrases like “32-bit” and “64-bit” refer to the CPU bitness of the underlying CPU, or CPU architecture, being referred to.
Indeed, early personal computers had 8-bit CPUs, which operated on a single 8-bit byte at a time. Operations that worked on values larger than what could be contained in a byte – a number between 0 and 255 – had to be broken up into multiple steps.
16-bit CPUs, popular in the early days of the IBM-compatible PC, operated on numbers between 0 and 65535, but once again, any operations on values that exceeded that range had to be broken into multiple steps.
32-bit CPUs soon followed, and at this writing, 64-bit CPUs are commonplace.
Naturally, it’s much more than simple integer math that’s impacted. As an additional example, the amount of RAM a CPU can actually access is impacted by it’s “bitness”. A 32-bit CPU, for example, can natively only access 4 gigabytes of RAM, in large part because a 32-bit number can only range from 0 to 4,294,967,295, or just over 4 billion. (8-bit and 16-bit CPUs often had to perform multiple-step operations in order to be able to access a useful amount of RAM.)
The structure of a CPU’s programming instructions, and the rate at which the CPU can process them, is similarly impacted by its bitness.