Is part of a computer's hardware that executes each instruction in a program?

The CPU, or central processing unit, is the hardware that takes most of the load when running a program. It will perform complex calculations and execute every instruction as the program continues.

The GPU, or graphics procession unit, is the hardware that could also play a major roll in calculating the instructions to execute a program, though this depends on how graphically intensive the program is. For example, games would use a lot more GPU power than say a simple calculator application.