What does the recovery system do on a model rocket?

It basically allows you to reuse your rocket. Common recovery systems are a parachute or a streamer, both of which pop out of part of the rocket (the nose, usually) when it's in the air. The parachute (usually used with slightly larger rockets) or the streamer (generally found on smaller rockets) then catches the wind/air as the rocket comes down, allowing it to land without damage.