How do supersaturated solutions demonstrate conservation of energy?
To make a supersaturated solution, usually you have to apply heat to get the excess solute into solution. When the solute precipitates, such heat is evolved.
A supersaturated solution is a solution that contains MORE solute than the amount that would be in equilibrium with undissolved solute. Supersaturation thus describes a metastable, non-equilibrium condition.
To get the excess solute into solution, normally you would have to apply heat to get the solute up. After cooling, when a seed crystal is introduced, this heat is noticeably evolved. Given that the heat put into the system, to dissolve the solute, is evolved when the solid comes out of solution, conservation of energy is satisfied.
Note that years ago, they used this principle to heat railway cabins on overnight trains. They had a large quantity of sodium thiosulfate in water in a can, which they would heat up to supersaturation point, and when they wanted the cabin heated they would add a crystal to precipitate the solute, and evolve heat.
Please note that the given definition of supersaturation is one that you must simply learn. Your teacher should show you this principle during a practical session.