Turn based combat. You weaken the enemy and then you can imprism it kind of like catching Pokemon. By default you and your imprismed critters play as "stacked" i.e. standing on top of each other and you get 1 turn per team member using any of the powers available to you.
You can unstack and each member of your stack gets a turn but attacks seem to be much weaker.
You are probably going "Huh?" right now because you kind of have to play it to understand. You aren't given much in the way of instruction either so you need to figure a lot out for yourself.