What determines whether a microprocessor is considered an 8-bit a 16-bit or a 32-bit device?

The number of bits a CPU uses to represent integer numbers (as opposed to floating point numbers or memory addresses) is often called "register width", "Word size", "bit width", "data path width", or "integer precision".

This number is often considered one of the most important characteristics of a CPU.

Most CPUs are 8 bit CPUs. An 8 bit CPU -- i.e., a CPU where each register holds 8 bits -- typically has a 8 bit data bus and a 16 bit address bus.

One of the first 32 bit CPUs -- the MC68008 -- had registers that held 32 bits, a 20 bit address bus, and an 8 bit data bus.

Some popular 32 bit CPUs -- i.e., CPUs with registers that hold 32 bits -- had a 32 bit data bus and a 24 bit address bus.