At the triple point of water all the three phases of water i.e. solid liquid and gas exist in equilibrium.According to chemical equilibrium "Equilibrium" may be defined as the rate of forward reaction is equal to rate of backward reaction in a chemical reaction. But at the triple point of water what does equilibrium mean??

It means the same thing. Type three letters G, L, and S at vertices of an imaginary triangle, connect the letters pairwise with forward and reverse reaction signs (as in chemistry). This is what is going on at the triple point: all three phases are turning into each other constantly, with no accumulation of any phase in particular.