"The holographic principle is a property of quantum gravity and string theories that states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind[1] who combined his ideas with previous ones of 't Hooft and Charles Thorn.[1][2] As pointed out by Raphael Bousso,[3] Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. In a larger sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure "painted" on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies."
So the analogy is that the field inside the volume can be completely described by some function over the bounding surface of the volume, similar to how the light field captured by a hologram is projected and recorded on a flat glass or film plane. I can visualize that pretty easily, but I don't know enough to tie that to some concrete relationship to the fundamental physical forces of the universe.