Upon a slingshot maneuver to allow CASE and Amelia Brand to arrive on Edmunds, Cooper and TARS detached themselves from the Endurance and fell into the black hole Gargantua. They were both seemingly rescued by the bulk beings and brought into their three dimensional representation of five dimensional space. The Tesseract allowed Cooper to communicate with Murphy Cooper in various time periods, presenting time itself as a physical dimension rather than linear. Everything is linked by the strings of time, which Cooper can manipulate. The beings made this comprehensible to Cooper by allowing him to physically interact with the Tesseract. Every push of a book from him was communicated to the appropriate time period with gravity, and when he touches the "strings" of the watch he gave his daughter, he can cause its hand to twitch from the moment he does so for the rest of its existence in time itself.
Cooper realizes that he was in fact Murph's "ghost" all along, and that while the bulk beings can perceive five dimensions, they cannot locate a point of reference in time; however, he can due to his connection and love for his daughter, drawing him to her much like gravity draws things to itself.
When the bulk beings close the Tesseract, Cooper speculates to TARS that they are not aliens but humans from millennia in the future, from a time when humans have evolved to a point they are able to harness untold amounts of energy and possess access to the entire universe.