Originally Posted by
BillyKaplan
From the lore book about Arcanima:
"A form of arcane art using esoteric calculations, arcanima was developed originally by the people of the south sea isles. After discovering a means of expressing natural phenomena in mathematical terms, they refined formulae into arcane geometries - precise patterns that allowed practitioners to weave aether into specific magical effect. This, in turn, bore the school of arcanima."
Like Tillie said, Arcanist utilize geometrical patterns inscribed with special, aether-conductive ink. When they invest their aether into it, you receive the desired end result, be it a spell, or a summon. By changing things in the geometries, you receive different end-results, like the different Carbuncles.