Chipping is when you use a chipping wedge to hit the ball towards the green. Usually, you are very close to the green when you use a chipping wedge, because you will not hit the ball very far. A chipping wedge has a low angle, and will pop up the ball, but not far. You don't have to use a lot of power when chipping, rather you should use finesse. It is important that you hit the ball accurately because there are a lot of obstacles around the green like sand traps that could hurt your score.
Being able to chip the ball accurately is a very important skill in golf. When you are close to the hole, you can hit the ball with a chipping wedge. If you are the best driver ever, but don't have a short game (another way of talking about a golfer's skill while close to the green) you will not have success in golf. You must be a well rounded player to succeed.
To chip, there are a couple clubs you should use. There are certain clubs designed to hit the ball a short distance, which are all in the chipping wedge family. These include a pitching wedge, sand wedge, and 9 iron. All of these clubs have specific purposes, but all will hit the ball a short distance if you are close to the green. You also swing a little differently with these short distance clubs. Instead of the normal big windup, you should only lift your club about half of your usual windup.