In chess, the king is never captured—the player loses as soon as their king is checkmated. In formal games, most players resign an inevitably lost game before being checkmated. It is usually considered bad etiquette to continue playing in a completely hopeless position.
In chess, several checkmate patterns occur frequently enough to have acquired specific names in chess commentary.
In Anastasia's mate, a knight and rook team up to trap the opposing king between the side of the board on one side and a friendly piece on the other. This checkmate got its name from the novel Anastasia und das Schachspiel by Johann Jakob Wilhelm Heinse.
In Anderssen's mate (named for Adolf Anderssen), the rook or queen is supported by a diagonally attacking piece such as a pawn or bishop as it checkmates the opposing king along with the eighth rank.
Sometimes a distinction is drawn between Anderssen's mate, where the rook is supported by a pawn (which itself is supported by another piece, as in the diagram), and Mayet's mate, where the rook is supported by a distant bishop.
In the Arabian mate, the knight and the rook team up to trap the opposing king on a corner of the board. The rook sits on a square adjacent to the king both to prevent escape along the diagonal and to deliver checkmate while the knight sits two squares away diagonally from the king to prevent escape on the square next to the king and to protect the rook.
There are two points to why the Arabian mate is both unique and significant: 1) It is mentioned in ancient Arabic manuscripts. 2) It is derived from the older Persian form of chess where the knight and the rook were the two most powerful pieces in the game. This was before chess had migrated to Europe and the queen was (later) given its current powers of movement