Okay speaking from personal experience. I have a base station with a homebrew 11 meter antenna at my office.
It tuned perfectly at the antenna feedpoint, so I put it up. I ran some mini RG8 type coax I got from Ham Radio Outlet while I was in Anaheim, CA about six months ago. Its a fifty foot run. As groundplanes go, it tuned out perfectly as I said before. But there's loss and mismatch.
I got lucky and found a Zetagi antenna matcher. I think they call it a 27 (for 11 meter). I found it at a Goodwill store so lucky me it was 3 bucks. Since that time I have not been able to find a local distributor, as these come out of Italy. Anyway I digress. The matcher actually fixed my SWR problem and ironically matched the coax to the antenna, or more appropriately matched the radio to the coax and antenna.
To explain it is kind of difficult. Everyone else seems to have given you a good explanation. So here's the gap filler. Your radio is set for 50 ohm matching. In theory if you have a 50 ohm radio, 50 ohm coax, and a 50 ohm antenna, then everything matches and you should have very little signal loss and your SWR's if they are not dead-even should be close. But, nature isn't perfect. No matter how close they try and make coax 50 ohms, it isn't. Depending on a bunch of variables including technical velocity factors and such gobbeldy gook that is great for math geeks and those familiar with geometry, trigonometry and the standard model and special model of physics, its all Chinese and so you have to take my word for it here. Coax no matter how perfectly made will have an impedance value of say 34 to 36 ohms. So ... you get some loss. Some coax is more lossy than other coax. So there's a gap. And that gap between that 50 ohm antenna and 50 ohm radio is your SWR value that is the amount of energy going through the center conductor and returning back in the form of RF energy or heat through RF ground. You can't transmit out without it back firing to your unit. The idea is to get as much out as comes back on an even number. When more comes back to your unit, the hotter your transistor gets because now its mismatched, and it de-tunes. The hotter it gets the more detuned it gets and its possible to blow your finals. In the old days it was easy to blow your finals. Today's transistors are designed to take a load of abuse. But you can still damage them and detune them.
So what is the matcher? Its two variable capacitors to ground. Some are single capacitors to ground. It appears to short but in reality it bounces your signal back up to the radiating element instead of into your radio. In a way it tunes to resonance and in a way it doesn't. So its both a tuner and a matcher, but in reality its just a matcher.
A capacitor stores and discharges energy across either air or a membrane; and depending on which direction its going and how much, it will do a fine job of balancing your RF out to your RF back if you have the right one. What does not get emitted out, just bounces back and forth away from your radio, as the others said. No risk of detuning your finals.
If you do find a Zetagi I will say they're good for standard radios. I don't think they're rated for a lot of power but its an inexpensive item and works well for low power which is what I use it for. I am getting another one for my mobile radio because I have a stubborn antenna situation without any easy solutions.