How much chemistry do you want? I think E-Z-Est, one of the most commonly-used dips, is a dilute solution of sulfuric acid and thiourea. It works by "reducing" silver sulfide, the main component of tarnish, back to silver and hydrogen sulfide. Unfortunately, it can't return that silver to the coin in its original state, and (apparently) it can slowly attack the actual silver surface of the coin if you leave it long enough. Here's a thread with more discussion.