It is all about a rotating system of stats. Basically you have your basic attack, Psynergy (spells) etc. But there are Djinn to collect (little monsters), up to 7 of each element. Using a Djinn in battle has a unique effect that differs per Djinn (each is unique). Once used they are 'set' and can be used as fuel for summoning.
The downside is that they also give passive buffs when NOT used, allowing you acces to higher stats, spells and even other classes.
Give protagonist Isaac, who's an Earth user, full Fire Djinn as a setup he'll become a Berserker Class, which has very powerful Psynergies, high attack stat and tons of HP. The differences can be monsterous. A level 40 Felix will have around 1000 HP and 710 attack as a Chaos Lord class, but give him 0 Djinn and he barely has 350 HP and 300 attack. So using Djinn to fuel summons is great for massive damage is fine, but you sacrifice damage output and defences greatly afterwards.
The Djinn system is all in really cool, always gives the feeling of "hm, what if I do this" when toying around with it. The biggest downside is that the game is too easy, meaning even if you barely use the system and just spam Djinn and Summons you'll most likely win (outside maybe one or two rare and hidden boss fights).
But all in all, great series. Adorable sprites too and godlike music. I'll never tire of the theme of Saturos. Anyone here ever played the games?
Here's an example of the combat (just googled a random boss vid, nothing special):