Back-rank mate
A back-rank mate is checkmate on the eighth (or first) rank when the king is trapped behind its own pawns.
The pawns that keep the king safe from checks in front also take away its flight squares. A rook or queen on the back rank then mates because the king has nowhere to step and no piece can block on that rank.
Ra8# is the whole idea. The king on g8 is boxed by f7, g7, and h7. There is no luft — a flight square created by moving a pawn to h6 or a6.
The coach warns about the back rank when your king has no luft and the opponent has a rook that can reach the eighth. One pawn move, or a rook left at home, is usually enough to prevent it.