The term gemstone isn’t a science word but is more like a cultural concept and not so simple to define, not even by gemologists (I checked).
Although they are usually crystalline minerals, gemstones are a category that also includes some uniquely decorative rocks, such as lapis lazuli, obsidian, mawsitsit. Gems may also be made of organic material, like amber, jet, ivory, coral, pearl and mother-of-pearl.
Some gems seem to be difficult to pigeonhole, such as opal (said to be an amorphous mineraloid) or ruby-zoisite, jasper and jade, which have been described as being somewhere between minerals and rocks.
Whatever sort of material they are, gemstones are always beautiful. Skilled artisans bring out their beauty by cutting and polishing and otherwise altering their raw form. An emerald is a mineral specimen, and although it may be lovely in its natural crystal formation, it’s not really a gem until after it has been worked on and transformed for our uses.
Gems are also relatively rare and precious -- although preciousness and rarity is not always determined by a list of objective criteria. Basically gemstones are gemstones because human beings made them so, in one way or another.
We commonly think of gemstones as being the materials for jewelry, but they are also used to adorn many other items, such as boxes, frames, plaques, religious artifacts, etc. They may even be carved into small statues and other three-dimensional art.
Some healers lay gemstones on the body to align the chakras; others even prescribe swallowing crushed and powdered gemstones. It’s a strange idea to most of us, but on the other hand, I suppose most gemstones are essentially minerals, right? The Vedic astrologers of India have an especially wonderful belief system regarding gemstones, which asserts that we draw upon the powers of the cosmos when we wear the precious gems. Additionally, several eastern religions view minerals as being alive, the first stage of reincarnation.
I found this marvelous poem by Rumi, the great Islamic mystic:
I died as mineral and became a plant,
I died as plant and rose to animal,
I died as animal and I was man.
Why should I fear?
When was I less by dying?
Science is becoming more and more precise in identifying and describing the various minerals on earth (and beyond). I do love to learn about minerals, but for me, the old lore and symbolism of gemstones are even more interesting.