In a live sound environment there is always a tiny bit of feedback; some sound is going out from the speakers and then back in through the monitors. When things are working properly, however, it should be entirely inaudible. When something goes wrong and a mic starts picking up enough of the speaker that it starts going around and around, you have a problem. If it's bad enough that each time it goes around it gets louder, you quickly have very loud horrible sounds that can cause permanent hearing damage.
If you're running live sound, there are pretty much two kinds of feedback. In the first there's a mic that's turned up too high or too close to a speaker and it already almost feeding back. Then the musician moves a little, you turn up their monitor a little, or they put their fiddle down on the floor in front of the monitor, and suddenly you have feedback. This is the more common kind, and while it's hard to avoid entirely, it's also usually more annoying than dangerous. It also can give a warning signal, in that there's a characteristic ringing echoing sound of a feedback that is going around and around but isn't strong enough to get louder each time.
(If you don't already know what this sounds like, you should learn. One way to learn is to point a mic at a speaker and slowly turn it up. Keep your finger on the control and be prepared to bring it back down as soon as it starts to sound bad. You'll find you can get it to balance just on the point of feedback, where sounds that come in make several round trips between the mic and speaker, but don't run away from you getting louder and louder. Don't try this when you're bored at a gig and the sound person is busy with something else.)
The second kind happens when something is off, broken, or muted but still hooked up and turned up high. Perhaps you're trying to turn up a musician, and you can't figure out why you still can't hear them. Once you get them all the way up you notice that they're muted. If you reach over and unmute them, you can get dangerously loud feedback. Which means that if you're troubleshooting and you find a switch that's wrong, don't just flip it back to right; turn things down, flip the switch, bring them back up.
What do you do when you hear feedback? Your first impulse should be to undo whatever you just did. This holds for everyone: performers and sound people. If you just moved closer to a monitor back away. If you just turned a knob up, turn it down. If you just unmuted a hot mic, mute it again. Your second impulse should be, if the feedback is dangerously loud, to turn anything down that will make it go away. It's more likely monitors than mains, so turn them down. If it persists, turn the mains down. If it's only annoying, though, and not dangerous, turning things off wholesale is disruptive and overkill. In that case you need to find out where the feedback is and fix it.
The general idea of trying to locate a feedback source is that if you turn a knob down and the feedback decreases, it's somehow involved and usually the culprit. You can quickly try turning down each mic to see which one it is, but some prioritization can help. When you set up mics there were probably some turned up higher than the others. So start with those. If you don't remember this or weren't the one doing setup, start with quiet instruments and ones where the gain knob is turned up high.
Once you've located the feedback and turned something down to make it go away, you have the problem that you probably had things how the performers wanted them, and now they're too quiet. So you need to figure out how to bring it back to where it was without getting feedback. The main idea here are that you want the microphone to pick up as much of the instrument as you can and as little of everything else. So get the mic as close as you can put it without the musician bumping it, and adjust your monitor locations so the mic is pointing completely away from the monitor.
Overall, you want to move carefully, not respond to finding problems by immediately fixing them, learn to recognize the sound of imminent feedback, and pay attention to whether mics are close enough to what they're trying to pick up.