CPU and GPU
The main processor in a computer is called the CPU - that stands for Central Processing Unit.
A lot of computers have a second processor whose job is to look after graphics, it is called the GPU or Graphics Processing Unit but most people refer to it as the Graphics Card. These can be part of the motherboard or on their own circuit board that can (fairly) easily be unplugged and a new one plugged in.
What is a processor
"A processor, or 'microprocessor', is a small chip that resides in computers and other electronic devices. Its basic job is to receive input and provide the appropriate output" techterms.com
The CPU's job is to tell all the other components in a computer what to do, based on the instructions it is given by the programs (software) that are running.To put that another way, the CPU executes (carries out / runs) programs using the fetch - decode - execute - cycle ( click for more on this).
You want your processor to be as fast as possible. Click here to learn how a CPU's speed is measured and other factors affecting how fast you computer can run processes.