I can't seem to get my head around spherical functions. I am used to thinking of functions as f(x) = y or similarly in multi-variable sense.

So, the point on a sphere in 3D can be described by the distance from the origin and the azimuth and the elevation angles. However, what does one mean when they say "spherical harmonics is only defined on the surface of spheres". Does it mean that the input to the function can only be the set of points that lie on the sphere or does it mean that the function has be represented only in spherical coordinates.

Really confused as to what exactly a spherical function is....