Angular Power Spectrum is a characterization of a function on the surface of a sphere, or analogously, all directions in space from a point. It captures variance as a function of scale, e.g., for some particular distance in radians, how likely is it that the two end points are similar. For example, it might show temperature differences (fluctuations) Kelvin as a function of degrees.
The Cosmic Microwave Background (CMB) is often characterized by the Angular Power Spectrum of its Anisotropy. The spectrum shows the calculated coefficients of a Multipole Expansion of the temperature over the spherical coordinates. In effect, it shows at what angular distances across the sky, calculated (Wien's Displacement Law) temperatures are similar. A Multipole Expansion is analogous to a Fourier Series expansion, but for functions on the surface of a sphere.
Initial Fluctuation Spectrum