Chemical equilibrium and stoichiometry
Let us take the example of your equation:
$$\ce{2SO3&lt;=&gt;2SO2 + O2}$$

The stoichiometric coefficients represent two facts:


If 2 mole $\ce{SO3}$ reacts, it will give 2 mole $\ce{SO2}$ and 1 mole $\ce{O2}$ but one needs to remember here that all of the 2 moles will not react. But the number of moles that do dissociate, give products in the above ratio i.e. if initially have 2 moles of $\ce{SO3}$ and degree of dissociation is 50%, then we will have 1 mole of $\ce{SO3}$ reacting to give 1 mole of $\ce{SO2}$ and half mole of $\ce{O2}$
The stoichiometric coefficients also provide the powers to which the concentrations of each compound will be raised to in the expression for equilibrium constant $$K_\mathrm c = \frac{[\ce{SO2}]^2[\ce{O2}]}{[\ce{SO3}]^2}$$