Anyway, the idea is roughly as follows (it's been a while since I worked on this stuff, so my apologies for some possible inaccuracies): let's pretend we live in a two dimensional universe and that this universe is a two dimensional quantum gravity theory, which is "asymptotically $AdS_2$", which is very similar to a hyperbolic plane $\mathbb H_2$ but of minkowskian signature (google it or stop reading). Or just think of $\mathbb H_2$. The "asymptotic symmetries" of $\mathbb H_2$ are such diffeomorphisms which preserve the metric near the boundary. For $\mathbb H_2$ these symmetries are isomorphic to circle diffeomorphisms $Diff(S^1)$, which is an infinite dimensional group. The only thing we need to assume about the quantum gravity theory is that it is integrable w.r.t to the asymptotic symmetries, which in this context just means that every physical state can be mapped to another physical state by the asymptotic symmetries extended to all of the space (a la Conformal Field Theory).
The toy model I used in the "Easy Holography" paper was basically just a pixelated image (of a bunny, since it was submitted on Easter). A rough estimate of the entropy of that "model" is then a logarithm of the number of all distinct images that are mapped from an original image by the asymptotic symmetry group, which is isomorphic to $Diff(S^1)$.