Audio feedback is the ringing noise (often described as squealing, screeching, etc) sometimes present in sound systems. It is caused by a "looped signal", that is, a signal which travels in a continuous loop.
One of the most common feedback situations is shown in the diagram below - a microphone feeds a signal into a sound system, which then amplifies and outputs the signal from a speaker, which is picked up again by the microphone.
To eliminate feedback, you must interrupt the feedback loop.
Here are a few suggestions for controlling feedback:
Feedback can occur at any frequency. The frequencies which cause most trouble will depend on the situation but factors include the room's resonant frequencies, frequency response of microphones, characteristics of musical instruments (e.g. resonant frequencies of an acoustic guitar), etc.
Feedback can be "almost there", or intermittent. For example, you might turn down the level of a microphone to stop the continuous feedback, but when someone talks into it you might still notice a faint ringing or unpleasant tone to the voice. In this case, the feedback is still a problem and further action must be taken.