Sure. I don't work in physics, but here is my understanding of the holographic principle.
Imagine that you are in a bathtub. There is a certain kind of physics that dictates the motions of waves in the bathtub. Now, you might believe that you need to understand the entirety of water to predict its future motion. You could develop a theory of water in bathtubs, and run experiments to verify if they are true.
After a lot of thought, you might come across the realization that in order to understand the mechanics of the water in the bathtub, it is only necessary to understand the way the surface of the water moves, or maybe even how the water interacts with the edge of the bathtub. This means that you've reduced the dimension of your theory in some way. While this analogy isn't true, there are examples of where it is-- for instance, the physics of harmonic oscillators, like strings, drumheads, etc, can be understood by looking at the boundaries of those oscillations.
Now, in physics, there are several ways that holography shows up. The most famous of these holography theories is called the AdS/CFT correspondence. It conjectures that a certain 5 dimensional string theory can be understood as a 4 dimensional field theory on the boundary. Now, I think that this perspective is interesting to physicists not because of the dimension change (dimensions in theoretical physics usually have little correlation with the observable dimensions of spacetime) but because it was one of the first known correspondences where a string theory reproduced the results of a field theory. Quantum Field theory is the most validated theory of physics we have, but it is thought to have foundational errors. String theory is suppose to offer a way out, but is... hard.
Hope that helps!