Spherical harmonics are basically a fourier series. They're a complete orthonormal set of basis functions for functions for the unit sphere. Whereas the fourier series from calc 101 is a complete orthonormal set of basis functions on the unit interval (eg [0,1]).
In other words you can express any reasonable function on the unit sphere as a series of spherical harmonic terms. That makes them ideal for working with differential equations (eg schrodinger's equation for the hydrogen atom, or, emission from an arbitrary light source).
In other words you can express any reasonable function on the unit sphere as a series of spherical harmonic terms. That makes them ideal for working with differential equations (eg schrodinger's equation for the hydrogen atom, or, emission from an arbitrary light source).