Basically, the job of a Ag/AgCl electrode is to convert (transduce) a chemical (ionic) current in solution into an electrical (atomic) current in a metal wire (or vice versa).

This transduction is achieved by the movement of Cl atoms on and off of the Ag metal wire. When a Cl ion binds to the Ag metal it donates an electron to the metal and when it debinds it takes one with it.