When you move a piece and enable another piece to check the enemy King, it is what we call a Discovered Check.
In practice, this tactic is often employed to gain material, catching an enemy piece with your moving piece.
At times, the moving piece may also deliver a check, or invade a strategic point resulting in immediate checkmate.
Examples 1 & 2
When Red moves the Cannon, Black has to answer the uncovered check by the Horse. Therefore, Red can win a Horse for free (and resolve the checkmate threat) with C3-7
The position looks similar to Fig 1. Red R3-6 discovered checks and wins a whole piece of Chariot.
Better still, he could have played the more aggressive R3=5. This cuts off the King’s escape route and wins the game at once.
In Fig 3, Red has a Chariot and a Cannon lined up at Black’s baseline but they do not post any checkmate threat. However, the position enables a discovered check by R2-8, winning a whole Chariot. Red will then have an easy road to victory.
In Fig 4. Red looks helpless against Black’s C1+1 or P2=3 immediate checkmate. Luckily, he is able to perform a Chariot-Cannon discovered check and destroy Black’s most aggressive central Pawn:
1. R2+7 A5-6, 2. R2-8 A6+5 (K5+1 will be met by R2+6 checkmate), 3. R2=5 .
Some of you may think that Red will win then. In fact, it can’t. Black’s has a good move here to draw the game. I leave it to you to explore the continuation.
I call this the Cannon-Chariot discovered check to differentiate it from the last example. Cannon is the moving piece, with the checking Chariot behind it in the lineup.
Red can perform a discovered check by C2=6 capturing an Adviser, or better still C2-1, winning the Chariot. Note that here Black cannot play E5-7 (for not serving the enemy Cannon as its gun carriage), as it will be met with R1=3, Royal Checkmate. F
Lastly, I have composed a little endgame study showcasing a total of nine successive discovered checks and captures that bring the final victory. Note that throughout the process, Black may not block the RC double-check with C6-8, as it will be met with R2=4 checkmate.