is an implementation of a Computer Organization (Microarchitecture - µarch - uarch)
executes instructions that make up a computer program (see Computer Architecture)
is part of a computer that fetches, decodes, and executes instructions, as opposed to memory, I/O, etc

CPU History

In the stone age days of computers, a mainframe CPU occupied multiple cabinets
Later a mini computer’s CPU occupied one or a few printed circuit boards (PCB)
The next step was to integrate a CPU on a single integrated chip (thus called a microprocessor)

From there the development forks:

microcontroller (uC) - is a CPU combined with memory and I/O on the same chip, creating a complete computer on a single chip
system-on-a-chip - a moderately powerful CPU (more powerful than those in a uC, but less than those in a desktop CPU) combined with a small boot ROM and a set of complex peripherals, like a video/LCD subsystem, MPEG decoder, wired or wireless ethernet interface, USB interfaces, etc. to create a ‘system-on-a-chip’. These chips form the heart of modern set-top boxes and the small Linux systems (Beaglebone, Raspberry Pi, etc.) derived from them
super-microprocessors - the CPU-on-a-chip is made more powerful (faster, parallel execution, fast execution of complex instructions like divide and transcendentals), a cache is added, more CPUs are combined in one chip, etc

CPU Brands