Crystallization usually starts when a liquid solution becomes fully supersaturated. This means the liquid holds more dissolved solid than it normally can at that temperature. It can also happen when a melted substance cools below its freezing point.
The loose particles naturally move toward a more stable layout with lower energy. The whole physical process takes place in two main scientific steps. The very first step of the process is called nucleation.
During nucleation, a tiny ordered cluster of particles forms in the liquid. The second and longest step is called crystal growth. In this step, more particles attach themselves to the initial cluster.
The growing crystal lattice strongly prefers particles of one specific size, shape, and charge. Because of this strict preference, the growing lattice leaves out most impurities. The unwanted impurities simply stay dissolved in the leftover surrounding liquid.
This makes crystallization an excellent way to purify solid chemicals in factories and labs. High school students often confuse crystallization with the simple concept of freezing. Freezing is just the act of turning a liquid into any random solid. Crystallization specifically requires the solid to form a highly ordered repeating grid.