Examples

The black king has no escape squares. If White checks with Qf8+, the queen no longer guards g5, and the king can escape.
However, White can check with g5+, forcing Black to play Qxg5 and blocking the escape square.
White can then checkmate with Qf8#.
Note that h5 is guarded by the Bishop in the final position.

Sometimes blocking the escape square can be combined with a deflection, as in the next example:

White can win with the deflection Qg8+.
Black cannot capture with the King, because the knight on h6 is protecting the queen.
Therefore, Black is forced to play Rxg8, blocking the king's last escape square on g8.
The rook is now deflected from guarding f7, and White can win with smothered mate Nf7#.

This combination of a deflection and blocking an escape square is a common way to reach smothered mate.

White can force checkmate with e7+!
If Black replies with Ke8, White can checkmate with Nf6#.
If Black captures either with Bxe7 or Rxe7, blocking the escape square, White can checkmate with Re8#.
Note how e7 also opened the diagonal b3-g8, so that the checkmating rook is now protected by the bishop.