Checkmating on the Back-Rank
Normally the King is very safe when the three pawns in front of it have not moved as shown in the following diagram:
However, if the King is checked in this position by a Rook or Queen (and it cannot be captured and nothing can be interposed between the checking piece and the King) checkmate results, as the King has no escape squares. This is shown in the following diagram. The White Rook checkmates the Black King.
Many tactics centre around this back-rank weakness.
In the following position White is down a Rook. However, Black's first rank is being attacked. White plays: 1.Qxe8+ Rxe8 (the only legal move.) and 2.Rxe8 is checkmate!
Look out for this sort of back-rank weakness in your own games!