it tells you the acidity constant (the equilibrium constant for the dissociation of protons from acids) and the solubility constant (the equilibrium constant for precipitating out of solution).
There are certain implications of the equilibrium constant. If the value is very large, over 1, the reaction is said to lie to the right (of the arrow) indicating a greater concentration of products; values less than 1 lie to the left higher formation rates of reactants, and values of one indicate equal concentrations. Knowledge of the equilibrium constant helps to determine, in an industrial setting for example, how to best produce a desirable material.
For example, in the Haber process for the formation of ammonia, the value of K is around 30 at pressures and temperatures standard for the process.
In an equilibrium between two conformers with energy difference 0, the equilibrium constant is 1 and both conformers are present in a 1:1 ratio. When the energy difference increases to 1 kcal/mol, the equilibrium constant at 25 °C becomes around 5 and the concentration of the more stable conformer gets 85%.