Primarily: To interface computers to virtually any electronic device. Be it to existing buses or high-speed connections (eg. a car's CAN bus, a console's controller bus), to small perhipheral electronic modules that provide desired functionality via I2C, or to individual components such as switches, lights, motors, and I/R sensors.
Less So: As a smaller computer that cause my code to interact independantly with the real world. Some examples include electronic furnace control and an autonomous (with only the barest hint of smarts) toy car.