Well, there is not much to really explain. That quote is kind of "self-explanatory," but I will do my best:
At this point in the story the man cannot take it any more. The beating of the heart (really the phantom beating in his own mind) is driving him up the wall. He realizes that he cannot live like this...it would lead to madness. He must admit his dead to the authorities in order to stop the beating.
Of course, the beating is really his own guilty conscience. This man must not have the true "heart of a murderer" because he can't live with the guilt. Of course, he probably wouldn't see it that way, believing the beating to be a phantom presence and not a psychological phenomenon.
I suppose you could make an argument that the beating actually was spectral, limited only to him, and that it wasn't his conscience forcing himself to admit guilt but rather that onslaught of some paranormal force driving him mad. That would probably make it a better horror story, but not a better story overall. In its incarnation about guilt it provides much more "food for thought."
I take it back...I guess there was more to say about this line than I thought! Kudos!
Love the irony here. The murderer thinks that the police hear everything and are just waiting him out for a confession when all along, they hear nothing because it is his conscience that is being plagued. When he feels he can take no more of their mocking and torturing, he yells out to them. Imagine their surprise when he confesses to a crime that they had no idea he committed! Not only does he confess, but he gives them the evidence as well. Poe at his finest as the real villain of the story calls the police "villains!" That was quite an easy case to solve.
The narrator was beginning to "hear" the old man's heart beat. The narrator thought that the police were trying to get him to confess, so he ignores the heartbeat for a little while. Then it is too much for him. He acts of a guilty conscience and shows them the hacked up pieces of the old man that the narrator murdered.