The term "tell-tale" is probably old-fashioned and completely out of use today. A synonym commonly heard in schools is "tattletale." Roget's Thesaurus contains many synonyms, including "informer," "stool pigeon," "fink," "rat," and "whistleblower." The idea Poe wanted to convey in the title was that the sound of the beating heart informed on the murderer and caused him to be apprehended. It is hard to think of what adjective Poe might substitute for "tell-tale" if he were writing the story today. He might call it "The Double-Crossing Heart," "The Betraying Heart," or "The Judas Heart." (On the other hand, he might just keep his origijnal title.) The sound, of course, was purely imaginary. It was most likely the murderer's own pulse he was hearing because he was feeling nervous and his heart was beating abnormally fast and raising his blood pressure.
The title acts as a bit of foreshadowing for this story because it is ultimately what gives the narrator away. He commits a murder and driven mad by what he believes is the heart of the murdered man beating beneath his floor. When the police arrive to investigate the crime, they are not there to arrest him, but he has already begun to be driven crazy by the sound of the murdered man's heart. The title then comes from his admission of guilt and plead to pry up the floorboards to reveal his crime. The heart will tell the tale of his crime- hence the title "A Tell-Tale Heart".
The unnamed narrator lives with an old man who has a spookily cloudy eye. The narrator appears to be crazy. He puts up with the old man for a long time, but the eye drives him further and further over the edge of insanity. Finally, one day, he murders the old man and buries his body under the floorboards. When police come to investigate (neighbors had complained of strange sounds coming from the house), the narrator believes he hears the old man's heart thumping beneath the floor. It sounds so loud to him that he confesses, screaming at the police: ‘‘I admit the deed!—tear up the planks!—here, here!—it is the beating of his hideous heart!’’
It is called "The Tell-Tale Heart" because the heart, he believes, has betrayed him and told of the narrator's crime.