In American Football pass interference is when a player interferes with an eligible receivers ability to to make a fair attempt to catch a forward pass. Pass interference may include tripping, pushing, pulling or cutting in front of the receiver or pulling on the receivers arms. It does not include catching or batting the ball before it reaches the receiver. Once the ball touches an eligible receiver the above rules no longer apply and the defender my tackle the receiver or attempt to prevent him from gaining control of the ball.
Once a forward pass is in the air it is a loose ball and thus any eligible reciever may try to catch it (all defensive players are eligible receivers). When a defensive player catches a forward pass it is an interception and his team gains posession of the ball. Some actions that are defined as pass interference may be overlooked if the defender is attempting to catch or bat the ball rather than focusing on the intended receiver.