The 4th Dimension!

The fourth dimension is time itself. We can travel anywhere in a three-dimensional space: north-south, east-west, and up-down, but we can only move forward in a four-dimensional space as we can only move forward in time. The relativistic laws guarantee it. In our lives we experience four-dimensional spacetime, three space dimensions plus one time dimension. To directly quote Kip Thorne: "At the simplest level, when we look out in space, we are automatically looking backward in time because of how long it takes light to reach us." This also explains how time dilation is even possible at all. With time being another perceivable dimension, it can be warped just as the other three can.

This concept is expanded upon in the movie when Cooper falls into a tesseract, a four-dimensional object built by an advanced people who solved the equation of gravity and learned how to fully harness it. And because gravity warps time, this meant the advanced people were also able to manipulate time as a physical dimension.

A diagram of the tesseract showing how time extrusions make up the 4th dimension of the tesseract.

However, Cooper is a three-dimensional being, so he is confined to the 3D faces of the tesseract unable to experience its fourth spatial dimension.