Explanation

In the biblical "Book of Samuel", the giant Goliath is defeated by young David.
With this metaphor, the pawn is David, and the king is Goliath.

This can also be less fancily called "pawn mate".

Examples

Black can deliver David and Goliath mate with g5#.
The rook on g2 protects the pawn, and also guards the escape squares g3 and g4.
The bishop on e2 is guarding the escape square h5.

White can deliver David and Goliath mate with e4#.
The pawn on d4 is guarding the escape square e5, the pawn on h4 guards g5, and White's king is guarding e4, f4, and g4.
Note that Black is unable to capture the pawn with dxe4, because the d-pawn is pinned by the rook on c5.