Black's bishop masks an attack by his queen against White’s loose knight on the e-file. Black looks for things he can do with his bishop that will keep White busy and allow QxN a move later. The bishop has no checks and no good captures; so Black considers everywhere the bishop can go, searching for a threat. He finds Bh3: not a check, but a threat against White’s rook. White either loses the knight or trades a rook for a bishop, forfeiting the exchange.
When you launch a double threat without a check at either end of it, as Black does here, you have to be especially careful to think about your opponent’s options in reply. Since you haven’t given check he will have a freer hand than he otherwise would; maybe he can give check, wrest away the initiative, and escape your attack. In this case Black needs to notice that White has a check available in Qa4. Is this trouble? No, because Black can meet it with b7-b5. But the point still holds: don’t go forward with a tactical sequence—especially one that doesn’t give check—without considering checks your opponent can throw at you in the middle of it.