The holographic principle tells us that the description of what happens in a volume of space can be encoded on a surface that surrounds it. This is related to the Bekenstein bound that tells us that the amount of information in a volume of space cannot be more than the area of the surrounding surface in units of a quarter of a planck area. This in turn as based on arguments that follow from the law for the entropy of a black hole in terms of the area of its horizon whichand the requirement that information is not lost in quantum mechanics. That black hole entropy law itself is derived from semi-classical calculations from the application of quantum mechanics to the black hole.
Although this long chain of arguments is considered plausible and well-thought through by many theorists it is also purely theoretical and has no empirical support other than what we know of the laws of gravity and quantum mechanics independently. The question is what would it tell us if we assumed it were true?
The answer is that it could tell us something about how quantum gravity works. Although string theory as a theory of quantum gravity seems to support the holographic principle in AdS/CFT, the exact nature of the mechanism has not yet been understood. It is possible that a deeper understanding of quantum gravity could explain the holographic principle (whether in string theory or some other theory). Alternatively, theorists could explore the holographic principle with thought experiments to reveal something about quantum gravity.
Since nobody yet knows the answer we can only add more speculation on top of the layers of speculation that led to the holographic principle in the first place. What I would say is that the field picture of what exists inside a volume of space must be full of redundant information if it can be equally well described by a theory on the surrounding surface as the holographic principle implies. Redundant information in physics is another way to talk about symmetry, so the holographic principle seems to imply that the field theory description must have a large amount of symmetry.
Classical gauge theories dont have enough symmetry to explain so much redundancy, but we now know that conformally invariant gauge theories have extra hidden dual conformal symmetries that can be described in the quantum theory of scattering. This lends credance to the suggestion that there is more symmetry our there that we dont know about. String theory in particular lacks a full description in terms of symmetries even though it possesses all kinds of symmetries such as supersymmetry and dualities, Perhaps the holographic principle tells us that more symmetry needs to be found before we can understand how it works.
Another line of reason due to Suskind is that holography implies a black hole correspondence principle where the experience of someone falling into a black hole is different from that of an outside observer but there is a correspondence between them and no contradiction. This correspondence was attributed to entanglement between the inside and outside of a black hole, and this in turn seemed to imply that the black hole horizon must have a firewall that destroys anything that tries to pass through. This seems to be in contradiction with the expectation from relativity that there should be no drama when crossing the horizon. It seems that the long chain of reasoning has therefore broken down somewhere.
Without any experiment to cross-check any part of the argument, every theorist has a different idea of what if anything has gone wrong. My take for what it is worth is that everything is fine up to and including the correspondence principle but that the explanation for that has nothing to do with entanglement.
I am not aware of any direct link between the holographic principle and fine-tuning or the multiverse. There is a very indirect link in that string theory may respect the holographic principle and it may also have a multiverse of solutions that account for fine-tuning.