Mate with two bishops
Checkmate is possible with two bishops and the king against a king. However checkmate is not possible with two knights and the king against a king.
Let me explain the two situations a bit more clearer...
1. Let's first check out the two bishops mate.
It is not too difficult for two bishops to force checkmate, with the aid of their king. Two principles apply:
a) The bishops are best when they are near the center of the board and on adjacent diagonals. This cuts off the opposing king.
b) The king must be used aggressively, in conjunction with the bishops.
Let me give you a situation: WHITE:Kd1,Bc1,f1 BLACK:Kd4
White to move. (Here are the moves, you can try them at a chess board)
1. Ke2 Ke4 (Black tries to keep his king near the center)
2. Be3 Ke5 (forcing the king back, which is done often)
3. Kd3 Kd5
4. Bd4 Ke6
5. Ke4 Kd6 (Black tries a different approach to stay near the center)
6. Bc4 (White has a fine position. The bishops are centralized and the king is active.
6... Kc6 (Black avoids going toward the side)
7. Ke5 Kd7 (Black is trying to avoid the a8 corner)
8. Bd5 (keeping the black king off c6)
9. Bc5 Kd7
10. Bd6! (an important move that forces the king to the edge of the board)
10... Ke8 (Black is still avoiding the corner)
11. Ke6 (now the black king can't get off the edge of the board)
12. Bc6 (forcing the king toward the corner)
12... Kc8 (Black's king is confined to c8 and d8. The white king must cover a7 and b7)
13. Kd5 (13. Ke7? is stalemate)
14. Kc5 Kc8
15. Kb6 Kd8 (Now White must allow the king to move into the corner)
16. Bc5 Kc8
17. Be7! (an important move that forces the king toward the corner)
18. Bd7! (the same principle as the previous move)
19. Bd8 (White must make a move that gives up a tempo. This move is one, along with Bc5, Bf8, Be6, or Ka6.)
20. Bc7+ Ka8