Controllers assist their allies with potent utility and keep enemies at bay with crowd control. Weak when alone, supports are capable of massively amplifying their teammates' power to become the strongest class in group combat (or teamfights), supplying crucial utility or crowd control at clutch moments to save allies from death and enable takedowns on the enemy team.
Supports typically start out by assisting the marksman in lane, as their own power is less dependent on items to function well, but over time their contribution expands as they lend aid to their entire team with both their spells and effective, yet affordable, items. Sub-classes of Controllers are enchanters and Catchers.
Catchers specialize in locking down opponents or, in some cases, entire battlefields by creating intense zones of threat that only foolish enemies would dare wade through. Although not as reliant on their friends as Enchanters, the fragile and immobile Catchers greatly benefit from allied presence - both to deter incoming danger and to help capitalize on targets they've locked down.
Enchanters focus on amplifying their allies' effectiveness by directly augmenting them and defending them from incoming threats. Enchanters themselves are often quite fragile and bring relatively low damage to the table, meaning they really only shine when grouped together with others.