Hitting a ball "Fat" means you got a hold of the grass behind the ball more than you should have. You usually end up with a nice divot behind the ball and your ball doesn't go anywhere near the distance it should have.
Then there is a "Thin" shot. This is where you don't get the iron completely under the ball and on the extreme end you top the ball.
The key is that the ball stikes higher on the club face than normal(opposite of thin where little of the club face is contacted), resulting in a loss of distance.