What is a gem crystal?

A crystal is a mineral which has a visible structure. Each mineral has its own particular favored structural form (six main classes of crystals that minerals will assume for a form).  Crystal form is very useful for determining what a mineral is (for identification).  Calcite, which often looks like quartz in color and clarity, likes to form a shape like a slightly squished rectangular box.  Well, when I see a six-sided pyramid, I know that it is not calcite, and think quartz right away.

A gem is simply a mineral that has value because people like the way it looks.  Most gems look best when they have made a well-formed crystal.  Some gems (like opal) do not form crystals though.  Others are not very attractive in the raw form (like rubies, perhaps), but can be "cut" along the crystal faces to bring out the shape of the mineral (get rid of the superficial irregularities and expose the underlying form).  Even diamonds tend to be pretty bland if the crystal structure is not exposed.

A gem crystal is a gem that is in its crystal form.  Not a mass of small crystals, not a crystal with irregular surfaces, but one which is exactly in the form of the crystal on the outside.

The form that the crystal takes is imposed by its chemistry.  The individual atoms have to fit together, and because there can be several types of atoms (elements) and several sizes involved, the structure can only be a certain number of ways and be orderly and repeatable in space.  The form of the crystal shows us how the atoms have arranged themselves; they are in that shape through and through, one giant building made from atoms all stacked together in the very same way, again and again and again.