This interesting state usually happens when a heated saturated solution cools down very carefully. Warm liquids can dissolve much more solid material than cold liquids generally can. As the hot solution cools, the extra dissolved solid normally wants to form crystals.
However, making new crystals from scratch requires a small burst of initial starting energy. This necessary starting energy is officially known by chemists as nucleation energy. If the liquid cools without any mechanical disturbance, the extra solid stays completely dissolved.
The solution now contains much more solute than the normal saturation point officially allows. Crystallization does not happen spontaneously because the solution lacks a good physical starting point. Any small physical disturbance can quickly trigger rapid crystallization as the system seeks balance.
Scratching the glass container or adding a tiny seed crystal provides the needed starting point. Once started, the excess solid crashes out of the liquid in a dramatic chain reaction. A common misconception is that these solutions are thick or cloudy before they crystallize.
In reality, a perfect supersaturated solution looks completely clear just like normal plain water. This hidden instability makes them very useful in classroom chemistry demonstrations and commercial heat packs.