The Suffocation Mate is a checkmate pattern with a bishop (or queen) and knight. The knight checks the king an the bishop suffocates him (with the help of a few enemy pieces that further obstruct the king).
Suffocation Mate Example 1
Diagram above: 1.Ne7# demonstrates the Suffocation Mate. The king is mostly obstructed by his own pieces and the white bishop covers the only open squares from a distance.
Suffocation Mate Example 2
Back in the year 1885, Wilhelm Steinitz, the first official world chess champion, used a variation of this checkmate pattern in a blindfold game! Steinitz played with the white pieces:
Diagram above: Black’s queen defends e7. If this wasn’t the case, then 1.Ne7+ would’ve been checkmate. That is why white plays 1.Rg3+, forcing the black queen away. 1… Qxg3 is the only way to get out of check.
Diagram above: Now that black’s queen doesn’t cover e7 anymore, white plays 2.Ne7#
The Suffocation Mate is related to the Smothered Mate.