When used properly bishops can be quite powerful. In many positions, a position can prove to be much stronger than the other minor piece, the knight.
What sort of position favors the bishop? Open positions, where pawns (especially central pawns) have been traded, tend to increase a bishop's potential. Bishops are best placed on open diagonals, where they can exert control over as many spaces as possible.
The diagram above comes about in a variation of the Danish Gambit (the moves played were 1. e4 e5 2. d4 exd4 3. c3 dxc3 4. Bc4 cxb2 5. Bxb2). White has sacrificed two pawns, but has compensation due to the two very strong bishops he has developed while Black was busy taking pawns.
While opening theory says that the position above favors Black (two pawns is a little too much material to give up, even given White's big lead in development), White's bishops are dangerous attackers thanks to the long, open diagonals they've been placed on. Black must defend accurately to retain his advantage.
