The Djinn are a HUGE part of the game, as well as what unlocks the class system. Though you can't start to find any of them until you leave the town. So, yeah, you should have just met Flint, and now you can start to find the rest.

Basically, each character has a number of different classes available, based on the element of Djinn they have equipped. Try swapping Flint to each different character and seeing how their stats and available Psynergy change. As you unlock more Djinn, you gain the ability to mix and match in more ways, and access more classes.