Chemical equilibrium is established when the forward rate of reaction is equal to the reverse rate of reaction.
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Explanation:

Equilibrium reactions are reversible reactions.

The general expression for equlibrium reactions is:

Which means that A produces B and B produces A. Those are two reactions:

So, in the direct reaction A is the reactant and B is the product, and in the reverse reaction A is the product and B is the reactant.

When you start with only A, only A is reacting and since the rate of reaction is proportional to the concentration of the reactants the rate of the direct reaction is high. As the reaction proceeds B appears and the concentration of A decreases, so the rate of the direct reaction decreases and the rate of the reverse reaction increases. At some moment the rate of both direct and reverse reactions are equal and the dynamic chemical equilibrium is reached.

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