How does photodiode works when use in reverse-biased photoconductive mode?
Conceptually, it is very simple. Photodiodes are just exposed PN or PIN junctions. Reverse biasing means there is an electric field over the junction. When a photon of sufficient energy hits the junction and is absorbed, this creates a free electron-hole pair which is accelerated towards the anode/cathode by the electric field, thus creating current. 

Visible light is coincidentally well-suited to this kind of operation, because the absorptivity of most semiconductors is fairly high in the visible region, while the required energy to excite an electron beyond the bandgap voltage is 0.6-1eV, which is exactly the amount of energy contained in a just-infrared photon (1200-1400nm). Higher energy photons (red, green, blue) get absorbed just as well, but the excess energy is converted into heat.