If a reversible reaction takes place in a closed system, where nothing can enter or escape, it can reach a state called dynamic equilibrium. At first the forward reaction is fast and the reverse reaction is slow. As reactants are used up the forward reaction slows down, and as products build up the reverse reaction speeds up.
At equilibrium the forward reaction and the reverse reaction happen at the same rate. Because of this, the amounts of reactants and products stay constant.
The reactions have not stopped. Both reactions continue all the time, with molecules being made and broken down at the same rate. This is why the equilibrium is called dynamic. The amounts of reactants and products are constant, but they are not necessarily equal.