This is the most common way of getting a batsman out. A batsman is out caught when one of the fielding players has caught the ball directly from the batsman’s bat. This means the ball did not hit the ground before the fielding player caught it.
Notice, the ball does not have to jump of from the bat; it also can jump of from the batsman’s pat. Also the ball may hit the batter below his wrist, to be counted as a full ball.
Also if the bowler catches the own bowling, the batsman is caught out. If the ball should be stuck in the batsman’s cloth or pads, he is not caught out and the ball will be claimed as dead ball by an umpire.
Should, in the rare case the ball be caught by a fielder when it crossed the boundary, the batsman is caught out. However, for this to happen, the fielder may not cross the boundary and may also not touch it. The fielder may cross the boundary with the arms but has to stay on the field with both feet. Otherwise the batting team will get six runs.