A fairly common attack-method in chess is to destroy the pawn shield in front of an enemy king (often with a sacrifice). This leads to various other checkmate patterns that become possible as a result of the open h-file.
H-file Mate Example 1
The examples below will show how the open h-file often precedes the execution of another checkmate pattern.
Diagram above: This position is known as Anderssen’s Mate, but it became possible as a result of the open h-file.
H-file Mate Example 2
Diagram above: 1.Rxg6+ hxg6 is a sacrifice that opens up the h-file. White wants to play 2.Rh8# on the next move. Note that if 1.Rxg6+ Rg7, then 2.Rxg7+ Kh8 3.Rhxh7# reminds us of the Blind Swine Mate.
Diagram above: Now that the h-file is open, white can execute the Morphy Mate on black’s king.
Interesting Note on the H-file Mate
The h-file is a common path of attack on a king-side castled king. Therefore, the H-file Mate is not really a checkmate pattern in itself. Instead, it’s a method of attack that often makes the execution of other checkmate patterns possible.