All right, so, there's basically two theories that we have in physics which we use to understand the galaxy, relativity for big things like stars and quantum theory for tiny subatomic particles, and the main difference between them is that gravity is a relevant force in the first, but not the second on account of it measuring things too tiny to have weight. The theory of relativity does a great job predicting where things will be and when (it's part of why GPS is so accurate nowadays), but it stops being useful in so-called singularities such as black holes where the mathematically based theory of relativity finds it's limit in the mathematically infinite variables a singularity represents. Such as gravity, as not even light can escape the gravity field of a black hole. That's significant because nothing is supposed to travel faster than the speed of light.
In the movie, humanity receives messages from 5-dimensional cosmic beings that communicate with NASA through gravity. Since scientists such as Michael Caine now knew that the manipulation of gravity was possible, they tried to reverse-engineer the concept in order to allow humanity to achieve interstellar flight. However, they were missing important information that the cosmic entities were already privy to, on account of existing in a state beyond human comprehension. That information had to do the variables of infinite gravity. At the climax of Interstellar, Coop and TARS end up flying into the singularity in order to rescue Brand. Surprisingly they don't die (presumably by alien intercession), and instead discover a place where time has been set up to be modeled in little 3D squares spread across infinity and all focused on a single location: Murphy's bedroom. Coop himself was the ghost who sent himself on his trip that ultimately took him to that wonky dimension, and after realizing that despite everything physics would tell us, he is able to influence the world outside the black hole from within it, he then has the robot translate the important science data into binary, and that's what he sends through the watch. Because he does so, his daughter has an epiphany about the nature of reality, interstellar flight is achieved, and humanity is saved.