[ajross]

It's the list of "waves" that can propagate around the surface of a sphere without interfering with each other. They are self-reinforcing modes. So you can represent any function of values on the surface as a combination of these, the same way you do with e.g. FFT coefficients in a JPEG file.

And it turns out that this "self-reinforcing" property is critically important for quantum mechanics, as each of the functions defines a different "state" from the perspective of a "particle". So we can do a lot of good physics work[1] by pretending[2] that all electrons exist in one of these states.

[1] Like, y'know, explaining chemistry.

[2] The details are always harder, because the electrons interact with other ways than just flying around the sphere, so the math isn't tractable in an absolute sense. But as long as you pretend that this is mostly right you can treat the remainder as just "fixups" in a giant framework called perturbation theory.