OK, I mentioned some character progression stuff, right?
You'll be able to equip a secondary class that corresponds to different magical elements. This is called an Affinity.
Having a higher level affinity equipped gives you bonuses (which increase with its level), but the main thing is that you learn magic spells as you level up your affinity. These spells stay with you even if you unequip it.
Each character will have unique skills that they can develop (which is what AP is spent on). Most of these skills require knowledge of specific magic spells in order to be eligible to acquire them.
You start off without magic. Early in the story, each party member will begin with their own individual Affinity. After the story opens up a bit, you will be able to change Affinity on command. As you progress the main story, new affinities will be unlocked.