Crystallization is the formation of an ordered solid structure from particles that were previously more dispersed.
Small ordered clusters form first. If one is stable, more particles can attach to it and the crystal grows.
In a solution, crystallization can begin after cooling or after some of the solvent evaporates.
Salt, rock candy and many laboratory purification methods rely on the same idea.
Growth rate, temperature, concentration and impurities influence crystal size and appearance. Slow, stable conditions often produce larger crystals.
A useful way to understand this phenomenon is to separate the driving force from the visible result. Temperature, pressure, concentration, surface area and the nature of the materials can each change the rate or the final state. In real systems, several of these factors often act at the same time.
That is why the same phenomenon can look different in a laboratory, in the kitchen or outdoors. The underlying chemistry or physics stays the same, but the conditions change the balance.