For starters all magic in the Sister Continents is Elemental in nature, whether the wielder is a sorcerer or a priest, but we'll get into that more later. It is also important to note that the Elements are not limited to those we think of on Earth... Fire, Water, Earth, Air. On the Sister Continents, magic is composed of fifteen different elements.
Gems hold a special place in the world of the Sister Continents in respect to Elemental Magic. The Elemental energies are particles which pass through every object on the planet, living or inanimate, and some gemstones will tend to collect these energies. The mechanism for trapping elemental energy is the crystalline structure of the gems, with different crystal structures prone to trapping different Elements. The structure of diamond, for instance, will tend to trap Elemental Life.
So, when you read of various types of gems in the books being related to a certain Element or power, this is not a random assignment. Every gem quality stone on Earth (396 as of my creation of the system a few years ago) has been assigned an Element or its structure does not support a particular Element.
This also means that when you see gemstones referenced, in the Tomes of the Touched as an example, one can glean clues to their symbolic meaning or potential uses just from the gems mentioned.
However, these tendencies are not set in stone for several reasons. Inclusions within a gemstone may effect its uses, heavy exposure to a particular Element during the stones creation can also change its powers, and gems can be enchanted with powers outside of the Element one might typically expect. A Diamond might well be enchanted with Fire, but the strength of the enchantment will be relatively weaker than if enchanted with Life.
More details will surely be released in the future, but for now, that's enough teaser spoilers without revealing the full system of the Mystic Lapidary.
As a writer's note, this set of rules can be rather annoying... Aesthetically, there are times I'd really like to use a particular gem as a symbol for an Element and it just doesn't work! Yes, any stone can be used with a particular Element, but symbolically, using the wrong one would either demonstrate an ignorance on the part of the culture or a flub/fudge on my part.