The first thing to see in this position is Black’s mating threat: his queen and knight both are trained on h2; with the knight also attacking the White’s king’s only flight square (f2), Black almost can play Qxh2#. Preventing this is White’s knight on f3, and Black has no immediate way to get rid of it. But he does have a rook on a3 aimed at the knight—through the pawn on c3. The knight is a sensitive target because of the defensive work it is doing, so the c3 pawn is relatively pinned. Another way to see this is to just ask what Black already attacks. The list is not long. His rook on a3 attacks the pawn on c3, and the c3 pawn has something good on the other side of it: the knight.

Since the c3 pawn is pinned, Black can toy with taking what it is supposed to protect: the pawn on d4. The idea thus is Bxd4+. Now if White plays c3xd4 (he must address the check), Black has RxN. Granted, the knight is protected, and trading a rook for a knight is not normally profitable. But you have to see the capture in light of the mating threat mentioned earlier: with his knight on f3 gone, White won’t have time to recapture because he has to fend off the threat of Qh2#. Black wins a pawn. (1. ...Nf3xBd4 is out of the question, of course, since it allows that same mating move: Qxh2#.)

There is still another way to see all this, naturally: just examine every check and see that besides Qxh2, which doesn’t quite work yet, Black has Bxd4+. The check is easily thwarted with c3xB, but the point is to see what the board looks like afterwards. The sequence opens a line for RxN, which is a clean capture for Black because of the fresh mate threat it creates.