[Bahamut2000X]

You don't get to use the system of the game till a few hours in when you get your first pieces of magicite, but basically the system works like this, you get these little rocks called magicite which are the condensed versions of magical beings, Espers, you equip one to a character and then you can summon that Esper once in a fight, but notably as you win fights you get AP (or something similar I forget the name at the moment) which goes into teaching your character spells associated with that Esper.

For example Bismarck teaches you Bolt, Fire, and Ice at a rate of X20, meaning for every AP you get, you have learned 20% of those spells. When you hit 100% your character knows the spell and can cast it.

Also some Espers give you stat bonuses on level up if you equip them. So a lot of people use that when they level characters to try and max out their stats as much as they can.

Hopefully that all made sense.