Edgar Allan Poe is renowned for his dark and twisted tales. Readers familiar with his works expect the text to be filled with madness, murder, and the supernatural. His texts, therefore, are filled with tension--for both the characters and the readers.
In regards to "The Tell-Tale Heart," tension exists for a couple of reasons. First, the narrator is utterly unreliable. The narrator opens with nervousness about his story. Immediately, he asks his listener (probably a doctor) about thinking him mad. This conflict creates tension between the reader and the narrator based on the fact of the suspicion of his madness.
Secondly, tension is created based upon the unrealistic idea of hating an eye. Readers tend to question the narrator's hatred of the old man's eye and the lengths the narrator goes to in order to rid himself of it. For readers, the idea of murdering over an eye is mad. Some may question why the narrator looks upon the eye every night given his hatred of it.
Regardless of how tension is built, readers agree that tension fills the story. From the nightly visits to the old man's room, to the actual murder and burying of the old man, the narrator's own tension fills the reader with tension.