When a player moves a piece A, it enables another piece B to attack an enemy piece. This is called a Discovered Attack. When it results in a check by piece B, it is then known as a Discovered Check.
The discovered attack can be very powerful, as the moved piece A can make a threat independently of piece B, and the opponent is unable to meet two threats at the same time. This tactic can be used to gain material or tempo.
The position in Fig 1 often occurs in the opening stage of a game. The Black Horse’s attack on Red’s Chariot is blocked by its own Pawn at the moment. Black can charge the Pawn accross the river resulting in a discovered attack.
Fig 1a is the position after Black P7+1. Since his Chariot is now en prise, Red has no time to deal with the embarked Pawn.
Fig 2. Red has just played R3+1 capturing a Horse. He is one piece up at the moment. Without any delay Black replies with C5+4 (a capture and check) resulting in a discovered attack from its right Cannon. In this example we may describe Black’s move as a discovered attack with check.
Fig 2a is the position after Black C5+1. As Red has to get his King out of check first by H3+5, Black will happily continue with C2=7, exchanging a Horse and a Cannon for the invading Chariot.
Examples 3 & 4
You should be able to perceive the opporturnity of a discovered attack available to Red in these two examples.
Fig 3, Red P3+1!
Black’s Chariot is burdened with protection of two pieces. If he captures the embarked Pawn with the Chariot, he will left the Horse en prise and fell prey to the Red Chariot next move. Whereas if he takes the Pawn with the Elephant, he will likewise lose the Cannon.
Fig 4 Red C2=7 threatening immediate checkmate and wins a whole Chariot next move!