The holographic principle is a physical property of quantum gravity theories, proposed by Gerard ‘t Hooft and Leonard Susskind, which resolves the black hole information paradox. It has been given a precise mathematical formulation within string theory, largely as a result of Susskind’s work.
The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that the description of all the objects which will ever fall in is entirely contained in surface fluctuations of the event horizon.
In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, so that the three dimensions we observe are only an effective description at low energies. Cosmological holography has not yet been made mathematically precise, partly because the cosmological horizon has a finite area and grows with time.