Backrank mate (1 move)
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Explanation
The back-rank is called "weak" if no major pieces (rook or queen) are protecting it.
The king starts on the back-rank and usually stays there until the endgame. An unprotected back-rank allows the opponent's heavy pieces (queen and rooks) to attack the king from the side, leading to a forced back-rank mate, or winning material.
Examples
Black can deliver back-rank mate with Rb1#.
Sometimes other pieces can help with the back-rank mate:
Here white can deliver back-rank mate with Rf8# The bishop on d6 protects the rook, and the queen on d3 guards the escape square on h7.
Pattern matching
The opponent's king is on the back-rank, with the escape squares on the next rank being blocked or controlled by your pieces. The back-rank is unprotected, protected insufficiently, or the pieces protecting it can be lured away.
A similar checkmate can happen on the a or h-file, see "high-striker mate".