I am assuming that you are referring to the scene in which he was enveloped in the tesseract inside the black hole with TARS.

He states in that portion of the film that the They (architects of the tesseract) is really a We. The tesseract was a physical manifestation of 5+ dimensions (X, Y, Z, Time, and a fifth dimension transversed only by gravity that until the singularity of the black hole could be crossed could not be fully understood). By entering the black hole, the data necessary to more fully understand the fifth dimension was acquired (by TARS who relayed it to Cooper who in turn through the tesseract relayed it to his daughter via morse code by interfering with the gravity affecting the second hand of the watch). Thank goodness he had a smart daughter. With the needed information to essentially create a unification theory, I am assuming that she was able to act on the fifth dimension creating a worm hole and the tesseract in a weird recursive fashion where the relativity of time could be accommodated despite the incongruities of their respective timelines.

It's hard to wrap your mind around concepts that really, the film is taking educated guesses at based on some of the deepest understandings of physics we currently have (future generations may have a good laugh at our expense or marvel at our prescience). I try layering dimensions to build out the next dimension so it always looks like a cube. A bunch of X's gives us a Y dimension. A bunch of X&Y's gives us a Z dimension. A bunch of XYZ's gives us a time dimension. A bunch of XYZTime's gives us Dimension 5 (which would seem like alternate realities to me). But as I review descriptions of dimension 5 and on I know that I am completely off, so the layering approach is not a good approach beyond 3 dimensions.

The film still leaves a number of questions though. Here are a few stabs I am taking:
Why are they living at Cooper station if they have unified theory and can build tesseracts? It may be a science station or port positioned near the worm hole for a human colony that is now all over the universe.

How did Cooper get out of the black hole? The same way he entered the tesseract - by will of his daughter armed with a unified theory. She built the tesseract, she collapsed it once the data of the singularity had been conveyed and transported him to the worm hole near Cooper Station.

Why was Cooper so much older than Murphy? Because of the time he spent in black hole. His time passed MUUUCCCHHH slower.

Armed with the unified theory, couldn't she just transport him to a more appropriate point in time when she was not old? No. Gravity can transverse dimensions (including time), but that the only interdimensional aspect.

I'm sure there are other questions...