The main aim of badminton is to hit the shuttlecock with your racket so that it flies over the net and lands inside your opponent’s part of the court. When you do this, you win a rally. If you win enough rallies, you finally win the match.
Your opponent is also trying to win rallies against you, trying to get your shuttle back over your side to land in your part of the court. You can however, also win rallies through mistakes your opponent makes! Should they hit the shuttle into the net, out of the court or under the net, you win that rally.
As soon as the shuttle hits the floor, the rally is over. This is different to tennis or squash, where the ball is allowed to bounce. You can only hit the shuttle one before it goes over the net, so this is different to other sports such as volley ball, where more than one player can touch the ball before it goes over the net (this applies in doubles too).