Feedback comes in two forms: positive feedback and negative feedback. Generally when someone refers to "feedback" they mean positive feedback.

In positive feedback, the signal (I'll use the example of sound) is picked up by the microphone, amplified by the desk/amplifier and emitted from the speakers. This sound is then picked up by the microphone to be amplified again and so on around the loop. Very quickly this positive feedback leads to a loud screech through the sound system (this is often bad for the speakers).

In the case of negative feedback, the signal received is subtracted from the input signal. This is very common in circuit design but has little application in sound reinforcement.