Microcontrollers are computers that have the bulk of their components all on one chip. A microcontroller can also be called a System on a Chip or SoC. What's so great about putting everything on a chip? You end up with a small, inexpensive computer that can do great things.
Can we hook up...
Press button
Joystick
Distance sensor
Motor driver
LED
Seven segment display
Rainbow strip
Dot matrix display
Speaker that beeps
Speaker that plays songs
This is the ATmega328P processor that lives in the middle of an Arduino Pro Mini compatible circuit board. This processor can be programmed using the Arduino IDE described here.