When :delta: G = 0 the system is at equilibrium. What this means more or less is that the rate of the forward reaction and reverse reaction are the same at this point so that, even though both reactions still take place back and forth, you don't see any net change taking place in the amounts of chemicals present. If you have a negative :delta: G the system is out of balance, and so reactants are spontaneously converted into products until the :delta: G reaches zero at which point you again see no net change. Conversely, if the :delta: G is positive then the products are spontaneously converted back into reactants until :delta: G reaches zero where you again see no change.