A tesseract is a four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells.
It is the four-dimensional hypercube, or 4-cube as a part of the dimensional family of hypercubes. The table of polygonal orthographic projections shows the massive increases in complexity as dimensions increase.
These structures are used in the understanding and physics of higher dimension cosmological structures and faster-than-light or time travel devices.
Interstellar contained a 5-dimensional tesseract created by future humans, and within was a 3-dimensional structure so that it could be understood and navigated by current humans.