And the reason it is so hard to wash off (you generally have to remove the skin itself) is that not much of the silver salt reacts and produces silver metal till it has diffused into your skin. It then attaches to molecules, particularly proteins with exposed sulphur atoms. At that point ist still is largely pale or colourless, but light soon reacts with the silver and removes it from its compounds and deposits it as a metal.
That part of the reaction is related to the process of photography, as it used to work before digital photography became popular. Before this happened people were becoming worried about our supplies of silver. Nowadays we have nothing to worry about except the supply of electrons.