Feedback is when a system output is routed back and becomes part of the input. This helps control the system and it is referred to as a closed loop system.
Feedback is usually negative, that is the portion of the output signal is subtracted from the input signal.
A simple example would be a heating system, a room thermostat feeds back to the boiler, once the desired room temperature is achieved the heater will switch off. When the room becomes cool, the thermostat will switch the heater back on.
Amplifier circuits use negative feedback to reduce and control the gain, without the feedback the output would continually increase to distortion.