Explanation

This checkmate pattern is named after Harry Nelson Pillsbury.
A game Pillsbury - Newman reached this position:

Here Renaud and Kahn, in the book "The Art of Checkmate", give the following continuation (although Pillsbury won in a different way):
17.Qf3!! Qxf3 18.Rg1+ Kh8 19.Bg7+ Kg8 20.Bxf6+ Qg4 21.Rxg4#

The original Pillsbury's mate.
The bishop on f6 guards the escape square h8.

Examples

Black can deliver Pillsbury's mate with Re1#.
The queen on c7 guards the escape square h2.
The bishop can be replaced with a queen on the diagonal, and the pattern remains the same.

White can deliver discovered Pillsbury's mate with Bf7#.
The bishop discovers the mate from the rook and also guards the escape square g8.

Related patterns

In opera mate, a bishop protects the checkmating rook and also guards one or more escape squares.