LeChatelier's Principle states that an equilibrium system will respond to any change by trying to minimize that change.
If A <-> B then adding B to the equilibrium system will make some B go to A in order to reach a new equilibrium. You can also think in terms of the reaction kinetics: at equilibrium rf = kf[A] = rb[B] . When you add B, the backward reaction increases (greater than forward reaction) until [A] builds up and [B] goes down and the rates are equal again.
Take care.