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In a discovered attack, or “discovery”, one of your pieces moves out of the way of another piece, unleashing attacks on two opponent’s pieces at the same time.
In this example, the white Knight moves to d4 square (Nd4+) out of the way of the white Queen. This unleashes 2 attacks at the same time: white Knight in d4 attacking black Queen on b3, and white Queen on f1 checking black King on f8. Black has to get out of check, and white captures the black Queen.
In the top example, the black Bishop moves to c4 square (Bc4+) out of the way of the black Rook. This unleashes 2 attacks at the same time: black Bishop in c4 attacking white Queen on f1, and black Rook in d8 checking white King on d1. White has to get out of check, and black captures the white Queen.
In bottom example, white move pawn to e5 square (e5) attacking black Queen on d6. At the same time, the pawn moves out of the way for white Queen on h4 to attack black Knight on a4.
In this example, white Knight on f3 is defending d4 square. Without this white Knight, black can move Bishop to d4 square (Bd4+) to check and creates a power fork to capture white Rook on a7.
Black can remove the Defender (white Knight on f3) of d4 square by capturing it with the black Rook (Rxf3).
If white responds by capturing the black Rook with pawn (gxf3), then black moves Bishop to d4 square (Bd4+) to check and creates a powerful fork to capture white Rook back. If white responds by not capturing the black Rook, then black just gains the white Knight for free.
This is a fantastic sacrifice of black Rook to gain a Knight.