Saturated, unsaturated and supersaturated refer to three different conditions of a solution.
A saturated solution contains the maximum amount of solute that will dissolve at that temperature. Any further addition of solute will result in undissolved solid on the bottom of the container.
An unsaturated solution contains less than the maximum amount of solute that can be dissolved at that temperature.
A supersaturated solution contains more than the maximum amount of solute that can be dissolved at that temperature. It is unstable and the solute will usually begin to crystallize, especially if disturbed.
Solubility varies with temperature. Most substances are more soluble at higher temperatures. A supersaturated solution can be prepared by preparing a saturated solution at a higher than desired temperature then allowing it to cool, decreasing the solubility of the solute.
Reusable sodium acetate hand warmers use the principle of supersaturation. They contain sodium acetate and water in a sealed packet. They are "recharged" by boiling, which dissolves the excess sodium acetate. When cooled to room temperature the solution is supersaturated, but is more stable than most supersaturated solutions. There's a small metal concave disk in the solution that when clicked creates a vibration that crystallizes the excess solute, releasing heat that warms the solution in the packet.