An arrow that points in both directions in a chemical equation is showing that the reaction is reversible and can proceed in both directions. This means that the reactants on the left hand side are also the products of those on the right and vice versa.
It is incorrect to write out a reversible reaction as two separate chemical equations (one for each direction) because the products always react and revert back into the original reactants. Because both reactions happen simultaneously, the chemical system is in a state of flux until equilibrium is reached. This means that there is a point where the concentration of each reactant remains constant and exhibits no net change over time. This does not mean that every reactant is present in equal proportions, though.
The rate of reaction and reaction coefficients of each reactant determines how much of it is produced and how quickly. Because some reactions are faster and require larger amounts of one reactant than another, they are not present in even amounts when the system reaches equilibrium. In dynamic equilibrium systems, the rates of reaction for both sides of the equation are exactly the same, so the concentrations of the reactants and products remain constant even though both reactions continue to proceed indefinitely.