Ok, I can understand that as the silver cation precipitates out, another cation comes to balance it.
But for copper (another cation) precipitates out, why does an anion balance it? Is it becuase it lost an electron?
As Copper precipitates out, positive charge will begin to accumulate at the anode, the anions will be attracted to this charge.
As long as you have your salt bridge maintaining your charge balance, the battery can continue to move electrons through oxidation/reduction reactions, you can derive electrical energy from these reactions.