Black’s knight on e5 is pinned to his rook. This causes Black to ask what offensive threats either his pinned or screened piece could make by leaving their squares; he searches for one that would buy time—just a move—that would allow him to take the other piece out of harm’s way, too. In this case the answer is easy if you practice an awareness of any loose pieces on the board, for then you are drawn to White’s bishop on c2. It is a simple matter for Black to attack it with his rook via Rc8. Now if Black’s knight gets taken, so does White’s bishop. If White doesn’t like this, he can move the bishop—but then Black has time to move his knight. The pin is ruined.
That’s the simple answer. A more complex possibility is worth noting as well. Suppose Black instead plays NxN. Does this break the pin? Consider this as an exercise; the answer will follow in the next paragraph.
Okay, the answer is yes. The risk, of course, is that White will reply with BxR; the question is what reply you could make to this. You look first for a check and see Qc5, a move that also has the useful feature of attacking the loose bishop on c2. This check forces White to either move his king back to h1 or interpose a pawn at d4. If White chooses Kh1, Black has NxBb8—and now he has won two pieces for his rook. White still has QxN available, but then Black still has QxBc2 as well, and after those captures he still has three pieces in return for a piece and a rook. It’s about the same if White instead replies to Qc5 with d3-d4. This time Black has to move his queen to prevent it from being taken, so he plays QxBc2 now and saves the threat of NxB for his next move. Once more Black ends up with two pieces in return for a rook.
But it's enough if you just grasp the basic principle here: the idea of breaking out of a relative pin by making a threat with one of the pieces involved in it.