The holographic principle is the idea that the universe is similar to a hologram, which is a projection into three dimensional space from information held in a two dimensional sheet. Although the universe is three dimensional, it is possible all the information describing its contents are encoded on its two dimensional boundary.
This idea originated from the study of Black Holes, which are the corpses of huge stars which have exploded and collapsed completely. Black Holes have such strong gravity that nothing can escape from them, not even light. A problem with black holes is that they appeared to break one of the most fundamental laws in the universe which is that information is neither created nor destroyed only transformed. But when objects fall into a black hole they seem to be lost to the universe. This problem was called the information paradox. The physicists Steven Hawking and Leonard Suskin had a famous disagreement about the information paradox and its solution, which became known as the Black Hole Wars. The solution to the information paradox is that, although the objects that fall into the black hole are lost forever, the information describing them is left behind on the surface of the black hole where, in principle, it is still available.
It was then realised that what may be true for black holes may also be true for the universe as a whole. In this sense we may be living in a universe which is a hologram.