Following

See the following references

http://booksc.org/book/9665757/25255e

http://booksc.org/book/44785875/e7c520

This is an excellent question. In addition to the very helpful answers already given, there is a bit more to add.

This question can be answered in terms of quantum entanglement (i.e., nonlocal quantum correlation). A quantum system is entangled, provided its state is not separable. It has been observed that quantum entanglement emerges from the holographic principle inasmuch as all information of a region (bulk bits) in spacetime can be described by bits on its boundary surface. An inside observer can describe the bulk physics with bulk bits.

By contrast, according to the holographic principle, an outside observer can describe only those bits on the boundary of a surface. Which are you? For more about this, see

Article Quantum entanglement from the holographic principle

A bit-thread representation of quantum corrections to entanglement entropy is represented in the attached image from

https://arxiv.org/pdf/1604.00354.pdf

In the attached figure, there are order N0 threads that can jump from one part of the bulk space to another, representing entanglement of bulk quantum fields. The ones that jump across the minimal surface m(A) contribute to the max flow on A and therefore to entropy S(A).

More to the point, we might want to ask What role does holographic entanglement play in the emergence of spacetime? A natural guess is the effect of bulk entanglement is to allow the threads to jump from one part of the bulk to another part (these threads are characterized as traversing Planck-sized wormholes connecting distant parts of the bulk), p. 23 in the paper by M. Freedman and M. Headrick.

Interesting question dear Alejandro Novo

The holographic principle is the statement that the spacetime we see around us is not a fundamental thing you put into a physical theory, but is reconstructed from the behavior of "matter". If you say it like this, it is a modernized souped up version of Mach's principle, which is something which motivated Einstein during the early years of General Relativity. But in the modern understanding, the word "matter" is identified with horizons, black holes. All the matter we think of as matter is either already a big black hole, like the black holes in the center of galaxies, or else it is a little quantum black hole, like the strings in string theory. The horizons of these objects form boundaries or edges to space time, and the holographic principle states that the right way to formulate the theory is on the boundary, on the horizons, not in the interior space-time.

The principle is extremely revolutionary, and I mean Copernicus, Heisenberg revolutionary, I don't think it can be compared to anything else in history, it is the most recent and arguably the most important single step that we have made towards the fundamental laws of nature. The holographic theories are the right way to describe quantum gravity, beyond any reasonable doubt, and this makes all older approaches obsolete, including ones that are still kicking around the literature. It essentially picks out string theory as the unique correct theory of quantum gravity, and for this reason, it has made some enemies among the politicians.

Before the 1990s, you formulated physics using space-time positions as the logically fundamental objects underlying your description (with one exception in the 1960s, which is related to string theory). Points in space-time were thought of as mathematical idealizations, like the real numbers, and the theories lived on top of spacetime, telling you what was going on at different points and the relation between these different events. The result of a quantum mechanical description of stuff going on at logically independent points is quantum field theory--- there is a collection of fields at every point which tell you what is the physical state of this point, and the dynamical laws give you the behavior of the quantum field in a background space-time. The classical limit of quantum field theory is classical field theory, or classical point particle dynamics (depending on the details of how you take the limit exactly).

But already within classical field theory, there was a hint that the physical description using fields was somehow limited, or incomplete. This is the following observation of Mach's: we can stand in an open field, and notice that our arms hang limply at our side. If we swirl around, the stars swirl around in our field of vision, and our arms get pulled out by centrifugal force. Then we stop swirling, and our arms are limp. Why should the distant stars and the local centrifugal force agree on what constitutes the non-rotating state?

Mach proposed that the reason is because the distant stars somehow had a role in defining what it meant for a local object to be non-rotating. The idea was primitive,but inspirational--- it meant that the local space-time was somehow related to the global configuration of matter. After relativity was discovered, Einstein reworked Mach's principle into the statement that the local notion of rotating/non-rotating (which is encoded in the metric tensor field) was the proper generalization of the Newtonian gravitational field, and Einstein hoped that classical General Relativity would give enough constraints on the gravitational field so that it would be determined from the matter configuration, and fix the local notion of inertial frames from the global configuration of matter.

General Relativity did do something like this--- if you look at an object surrounded by a rotating sphere of matter, the object will feel no centrifugal force when it is slightly rotating in the same direction as the sphere. The effect becomes more pronounced as the sphere gets heavier, and the inertia idea of no-rotation inside is asymptotically matched better and better to the rotation of the sphere when the sphere is just about to collapse to a black hole. This effect is called "frame-dragging", and it was an indication that there was some sort of Mach's principle in General Relativity.

But in General Relativity, this isn't really completely true. The issue is that there is another boundary--- the boundary far away--- determining what's the rest-frame, because there could be matter infinitely far away, thrown to infinity in the limit. So you can zoom into a point with a rotating black hole, and make the black hole smaller and smaller, then the rotation looks like it is relative to nothing, because everything else has been pushed out to infinity. So you must have a solution which is asymptotically flat with a rotating object in the middle, and indeed you do, this is the Kerr black hole. Einstein's response to this objection was that the universe should be closed on itself, like a sphere, and this motivated his spherical cosmology. In a spherical universe, you can't have a single rotating black hole, you need to balance it out with something else on the other side rotating too (although whether you call it "the same" or "opposite" direction depends on your perspective of how the rotations should be labeled). Einstein's universe is not stable--- the matter in this universe will collapse into black holes, and eventually, one of these black holes grows big and becomes the cosmological horizon, and swallows everything else, and the Einstein universe turns into deSitter space. This is important, because the deSitter space has as only matter the cosmological horizon (remember, this used to be a black hole). This means that you should not think of black holes and cosmological horizons as somehow second-class matter--- these things are matter like anything else.

Godel found a more weighty counterexample, the Godel universe. In this universe, the distant matter is rotating faster and faster as you go away from the center. The issue is that eventually the rotation is faster than light, and you can make closed timelike curves in the space. So this example wasn't so physical, but it was very strange, and it made it seem that Mach's principle was just a vague heuristic without a precise formulation.

In the 1960s, the development of S-matrix theory suggested that it was possible to make a quantum theory without using space-time notions. The idea was to use asymptotic plane-waves and their scattering to describe everything in terms of quantum transitions between asymptotic states. This idea was the first real method of making a theory without direct reference to space time, but when Feynman tried to do it, he ended up with another form of quantum field theory. Similarly, when Chew tried to do it for pions, he ended up with an effective field theory of the form of the modern chiral models, as understood by Weinberg.

But the S-matrix theory of Regge trajectories, unlike the theory of finite number of particles, did produce a new thing, and this new thing, string theory, included General Relativistic gravity in an approximation of low energies and small strings.

In this theory, the string objects can be identified with black holes in the classical limit (it's hard to make them classical, because this requires that you leave the regime where they are perturbative, but there are tricks--- you can use duality to relate strings to D-strings in type IIB string theory, and the IIB strings can be T-dualized to branes of different dimensions and then stacked to become black holes).

So in the string theory version, all matter is horizon stuff, it's a quantum black hole. The holographic principle is then the statement that the oscillations of this black hole reconstructs the space-time around the black hole, so that the entire theory is formulated on the boundary, not the interior. This is the precise version of Mach's principle, and in this form it is correct.

The understanding of the holographic principle is made precise in AdS/CFT, which gives precise examples of space-times reconstructed from black hole surface dynamics. It is a very strange duality, and it is a-priori impossible except that string theory does it. This is strong evidence that string theory is the only possible way to formulate a theory of quantum gravity. The holographic principle for string theory is much like the equivalence principle for GR, it explains why the theory must look the way it does.

To see why holography is important--- we now suspect that the N=8 supergravity theory is perturbatively renormalizable. Does this mean it is a possible complete theory of gravity as Dixon sometimes suggests? The answer is no, because it is s a field theory, it suffers from the usual paradox of field theory that when you form a black hole, it has infinite entropy. This is reflected in the fact that the N=8 theory looks like an inconsistent truncation of a string theory, but where the extra stringy stuff is pushed out to be very massive, so it doesn't influence the perturbation theory at any finite order. So the principle of renormalizability is not really what is selecting string theory, it is the holographic principle, and only the holographic principle. The S-matrix idea of the 1960s was a primitive version of this, because in the AdS/CFT correspondence, the CFT turns into the S-matrix in the limit that the space-time becomes flat.

Very rich and comprehensive information by Prof. James Peters and Dr. Beemnet. I also attach these very valuable resources on the holographic principle. Best regards