What is a crystal and how is it formed?

A crystal is a solid geometric structure of a repeating pattern of molecules connecting it together. In crystals, a unit cell is repeated in exactly the same arrangement over and over throughout the entire material.

Crystals grow by a process called "nucleation". Nucleation can start with assisted nucleation or unassisted nucleation. It will continue to grow until an equilibrium is reached.

Why crystals grow at different rates in different directions is a very complicated question. If there is a highly attractive interaction (energetically speaking) along a certain direction of a crystal, then that direction will probably grow fast. However, it could also grow slowly, if that direction interacted strongly with the solvent; having strongly absorbed solvent on the surface of the crystal could block growth.