Why do supersaturated solutions crystallize?
A supersaturated solution will spontaneously separate into pure crystals of the solute and a less concentrated solution because the free energy of the entire system (a combination of enthalpy and entropy changes) can be lowered as a result.
A supersaturated solution actually contains a higher concentration of solute than the equilibrium value, and the system always wants to lower its free energy by approaching equilibrium. The reason why you can form a supersaturated solution at all is because the kinetics of crystallization are sometimes slow enough to permit this temporary supersaturation condition.
Every system tends to want to minimize its enthalpy and maximize its entropy. The overall change in Gibbs Free Energy is given by
which is the balanced combination of changes in enthalpy and entropy that lead a system to seek equilibrium states.