Is the Universe really a giant hologram? The theoretical physicist Gerard 't Hooft suggested it might be in 1993. The essence of the Holographic Principle is very simple. It is all about encoding information from a space in "n" dimensions into a space of "n-1" dimensions. This is exactly what a holographic image does, allowing a view of a three dimensional object on a two dimensional surface, for example. In physics, one example is the theory that all the information about the history of a black hole, essentially its entropy, is encoded on its surface; that is, at the Event Horizon. The "bit" of information is represented by an area bounded on each side at the Planck length; that is ~10-66 sq cms. This could be extended to the whole Universe, if the Universe has an Event Horizon, which it would not have if dark energy theories prove correct. When an object falls into a black hole, it has two distinct existences. The first is inside the black hole, and forever beyond us. The second is coded as information on the surface of the black hole. In theory, with that information, we have a complete description of the object, though in practice we do not have any idea how!
The AdS/CFT correspondence was first proposed by Juan Maldacena in 1997; in fact, the theory is often referred to as the "Maldacena Duality". This states that quantum gravity in "n" dimensional Anti-de Sitter space (AdSn) is equivalent to a Conformal Field Theory in (n-1) dimensions (CFTn-1) that is defined on the boundary of the (n)-dimensional Anti-de Sitter space. M-Theory suggests that "our" world is a four dimensional space that is the boundary of a higher (10 or 11) dimensional space that is compactified into five dimensions. Thus, in effect, we are like four dimensional shadows of a five dimensional space. An often quoted example is the duality between Type IIB string theory in a five dimensional Anti-de Sitter space (AdS5), in the form of a five dimensional hypersphere, and a supersymmetric four dimensional Yang-Mills gauge theory (CFT4) on the four dimensional boundary of AdS5.
Unfortunately, once one goes beyond this description, the mathematics becomes extremely complex very quickly. Also beware of the "woo-woo" brigade who have started to hijack the theory as part of their mystical, pseudo-scientific babble.
Here is a view from Cambridge University, and another from Wikipedia. This piece from Universe Review uses some mathematics, but keeps it as simple as possible. There is also an interesting You Tube video (nearly an hour long) discussing the Holographic Principle. Here is a rigorous assessment of the AdS/CFT Correspondence; not for the faint of (mathematical) heart!