A Controller is any being who is controlled by a Yeerk in their head. Perhaps "Controlled" would be a more accurate term but it isn't the one that was chosen so get used to it.
Controllers can be any species with suitably large brain cavities, and they can be taken voluntarily or against their will. In an emergency the enslaved being can sometimes regain control for a few moments, but the price is great – Yeerks can carry on mental tortures for weeks. The only sure way to recognize a Controller is to watch him/her/it/etc for three galadays and see if the person attempts to go to a Yeerk pool.