A micro-controller is a computer! That is, it is a chip with a CPU (central processing unit), that has inputs, outputs and memory (RAM).
Micro-controllers are “special purpose computers.” They are made to primarily run just one program and perform one task (while the computer you and I are on is made to run thousands of programs). Because of this they are generally quite small and low power and low cost.
Micro-controllers are often embedded inside another device, often a consumer product. For example, a microwave has a micro-controller inside of it that takes input from the keypad and displays an output on the display and then runs a program that turns the power generator on and off.