If a chemical reaction happens in a container where none of the reactants or products can escape, this is a closed system. Reversible reactions that happen in a closed system eventually reach equilibrium.
At equilibrium, the concentrations of reactants and products do not change. But the forward and reverse reactions have not stopped - they are still going on, and at the same rate as each other.
Because they are taking place at the same rate (speed), the reactants are turning into products at the same speed as the products are turning back into reactants.
Imagine walking the wrong way on an escalator - walking at the same speed as the escalator but in the opposite direction. Your legs are still walking forwards, and the escalator continues to move backwards. However, the net result is that you stay in exactly the same place. This is an example of equilibrium. It is a dynamic equilibrium because your legs and the escalator are still moving.