That is where the derived part comes in. An equilibrium constant is actually a ratio of two reaction rate constants; the rate constant of the forward reaction and the rate constant of the reverse reaction. We say that a reaction is in equilibrium when the rate of the forward reaction is equal to the rate of the reverse reaction. For every two molecules of NO2 that react to form one molecule of N2O4, somewhere there is an N2O4 molecule falling apart to form two NO2 molecules.
So let's suppose that it is much faster for NO2 to react than for N2O4 to decompose - the forward rate constant is much higher than the reverse rate constant, and the Keq is a large number. For the forward reaction and the reverse reaction to occur at the same rate, you have to slow down the forward rate by making the NO2 molecules few and far between, and speed up the reverse rate by increasing the number of N2O4 molecules. At equilibrium, the concentration of product molecules is much higher than the concentration of starting material molecules.
If you try to increase the concentration of starting materials at this point by adding more NO2, you will speed up the forward rate even more and form more product, decreasing the amount of NO2 again until a new equilibrium is established, still in accord with the same Keq