Randomly grown silicon nanowire (SiNW) mats show a high light absorption even for long wavelengths despite the small volume of silicon. We present a statistical model that gives a physical understanding of the mechanisms of the absorption and scattering of light in such SiNW mats. According to this model the two main mechanisms of the effective absorption of light are (i) resonant optical antenna effects of the absorption within the individual SiNWs and (ii) the interaction of the light with several SiNWs in the mat due to strong light scattering. The results of this model are in good agreement with the experimental reflection, transmission, and absorption spectra taken with an integrating sphere.