Starting from the basics, crystals are materials made of closely packed atoms or molecules (the smallest unit of material) arranged in a very specific 3-dimensional pattern. As the pattern continues over large distance they form the geometric shapes that we see (think of a diamond, rock salt, or even a snowflake).

In general, crystal shapes are determined by the energy of the atoms (or molecules) in the material. Things always want to be in the lowest energy arrangement. Depending on the size, shape, and electronics of atoms or molecules, this leads to different patterns. Once a crystal pattern starts, it is almost always favorable for atoms (or molecules) to continue the pattern and grow into a crystal.

Crystals often need time to form these patterns, so most crystals are formed slowly over time. (Diamonds are formed over billions of years and crystals in caves are often formed over hundreds of thousands of years!) This gives the atoms or molecules a long time to find their place in the pattern (reach the lowest energy).

Sometimes there are multiple patterns that give low energies, like in snowflakes, so there are multiple crystal shapes for a single material.