Solubility is the ability of one chemical species to dissolve in another of the same or a different phase. In dissolution the solvent works to overcome the attraction of solute molecules to each other in such a way that the solute becomes distributed throughout the solvent. This requires that the solvent break the internal bonds and attractions of the solute and then form stronger interactions with the solute. If more solute is added than the solvent can interact with, the extra solute will form a solid known as a precipitate or a separate liquid layer, as when oil and water are mixed. At this point the solution is saturated.
Temperature is a measure of the internal kinetic energy of a substance. The higher the temperature is, the faster that molecules of that substance move on average. This kinetic energy can translate into molecular interactions such as collisions and bonding. Additionally, the increasing velocity of each molecule can create larger gaps between each molecule, especially when the volume of the substance is allowed to expand.
Higher energy collisions of solvent with solute, as in higher temperature solutions, cause pieces of the solute to separate and become freely interacting with the solvent. Thus, as temperature increases, the solvent gains more energy with which to break away and dissolve molecules of solvent. In some solutions, dissolution is limited by the distance available between molecules, as molecules will often repel each other due to electric charge. In these cases, the extra intermolecular space created by higher temperatures will allow more solute to dissolve into the solvent. In all cases, the higher average velocity contributes to an increased diffusion of solute, reducing local peaks of concentration and allowing the solution to more quickly become evenly saturated.
In a system with excess solute, a temperature change may cause a change in the overall equilibrium of the system. In most cases, solubility will increase with an increase in temperature, so the excess solute will dissolve into solution. On the other hand, a decrease in temperature can cause solute to precipitate out as the solubility decreases. If the temperature drop is rapid enough, the solute will not be able to precipitate out and the solution will become supersaturated. This kind of system is not completely stable, as more solute is dissolved than is normally allowed and a shock to the system may cause a rapid, and often violent, precipitation of the excess solute.