Look at this knight. Every one of the eight squares touching it is occupied, by both colours, and it has all eight of its moves available.
g A rook there would have nothing. A bishop there would have nothing. The queen, the strongest piece on the board, would have nothing. The knight has eight moves, because it does not travel through the squares between: it goes straight to the end of the L and appears there.
This is the one genuine exception to the rule that pieces cannot move through other pieces, and it is why 1.Nf3 is legal on move one with a pawn wall and a rook in the way.
Only the landing square matters
Two things follow, and they are the entire practical rule. Your own piece on the destination square makes the move illegal, exactly as with any other piece. An enemy piece there is captured, and everything the knight flew over is untouched. It does not sweep a row like a draughts piece and it does not take anything on the way.
The third thing follows from the geometry rather than the rule: a knight check can never be blocked. There is no square between a knight and the king it is checking, so the defender has to capture the knight or move the king. That is what makes smothered mate possible, where a king surrounded by its own pieces is mated by a single knight that nobody can get at.
Knights like the positions bishops hate
g When the pawns lock up like that, the bishop is looking at the back of its own pawn chain and the knight is not inconvenienced at all. Keep your knights in closed positions and your bishops in open ones, and you will make better trades than most players at your level.
The cost of the jump is speed. A knight needs six moves to get from a1 to h8, and four to reach b2. It goes over everything and it goes slowly, which is the trade the piece has been making since the game was invented.