Explanation

Balestra is the Italian word for crossbow. With this metaphor, the queen, king and bishop form the pattern of a crossbow.

Examples

White can deliver Balestra mate with Be6#.

Balestra mate can also be achieved with the bishop on an adjacent diagonal (instead of a criss-crossing diagonal as above), and even with the king not on the edge of the board, as this example shows.
Black can deliver Balestra mate with Bd4#.
Note that the bishop also protects the rook on g1 "through" the checkmated king. The rook is guarding the escape square on g2, so this is a rare Balestra x-ray mate.

Pattern matching

Sometimes this can be easy to overlook, because there are usually several checks available with the queen. If the queen is a knight jump away from the king, it already guards all or almost all escape squares - look out for any checks with your supporting pieces.

Related patterns

In Boden's mate, two bishops checkmate the king on criss-crossing diagonals.
In double bishop mate, two bishops checkmate the king on parallel diagonals.