It isn't clear to me whether AdS/CFT is simply a mathematical trick or whether it actually says something about the real world.
String theory has, for a while, been a primary candidate for a theory of quantum gravity. The problem is that it isn't easy to calculate with and it isn't easy to test. Both are problems for a scientific theory. One of the background geometries for string theory is anti-DeSitter space (AdS).
Most of modern particle physics is *similar* to some sort of Conformal Field Theory (CFT) and it turns out that the correspondence allows for easier computations on the AdS side that can then be translated back to the CFT model. In essence, it is easier to calculate in CFT for low energy situations (using what is known as perturbation techniques) and easier to calculate in AdS for high energy situations.
The holographic principle comes about because the CFT side has one fewer dimension as the AdS side. In essence, the CFT is on the boundary of the AdS. But the mathematical correspondence between solutions still works. This type of 'go to the boundary' technique works in many mathematical situations involving partial differential equations (which both AdS and CFT do).
At the very least, this AdS/CFT correspondence allows us to take mathematical solutions to one model and transform them into mathematical solutions in another model. Whether either of the models is actually useful is a separate matter.
And that is the basis of a LOT of criticism. Actual particle field theories are NOT conformal (only similar to conformal theories) and it isn't at all clear if some version of the correspondence deals with *actual* particle field theories. There is also a lot of doubt whether string theory is actually a good model of quantum gravity (partly because some of its predictions *seem* to be wrong--jury is still out).
TL;DR: AdS/CFT is nice math, but it isn't clear if it works in reality.