I think of it as a good basis for functions on a perfectly spherical surface. Going down in levels of "l", you describe more and more details in terms of angula

I think of it as a good basis for functions on a perfectly spherical surface. Going down in levels of "l", you describe more and more details in terms of angular scale. Thus, it's widely used in earth science and astrophysics, and anything that involves spherical symmetry (like a Hydrogen atom) -- in reality, nothing is a perfect sphere, but that's a very good approximation.