Few endgame problems are as difficult as the B+N vs lone-king. If the defender knows to retreat the king into the corner of opposite color of the bishop, no checkmate can be forced there. The attacker must force the defending king into the corner of the same color as that on which the bishop moves.
Watch this Youtube video on how to force checkmate in this end game.
Former World’s Women Champion fails to win endgame
In the Anna Ushenina v. Olga Girya game, played in the Geneva tournament of the FIDE Women’s Grand Prix 2013–2014, the former world women’s champion could not checkmate with bishop and knight against lone king. She apparently did not know the whole precise technique for winning that type of endgame.
Ushenina could have tied for third place in that tournament, if she had won that game against Girya, who appeared pleased that she had survived that game with a draw.
Technique for Winning This Endgame
Consider the position at the top of this post (with the black king in the h8 corner) and the following possible continuation.
1) Nf7+ Kg8
2) Bf5 (waiting move)
2) . . . . Kf8
3) Bh7 Ke8
4) Ne5! Kd8
5) Ke6! Kc7
6) Nd7! Kc6
7) Bd3 blocking the defending king from escape
The rest is easier for white. Theoretically this knight-plus-bishop endgame is a win, but it usually takes precise knowledge for a player to win against the best defense, in over-the-board competition.
With the move, can black draw?