A mage that focuses less on damaging enemies and more on coercing enemies into favourable situations for you and your team, often by threat or use of crowd-control (stuns, slows, charms, etc) ,displacement (knock up, knock back, etc.) or a combination of the two. Effectively, their intent is to 'control' the flow of a team-fight. Damage is usually a secondary for them.
Anivia, Azir, Cassiopeia, Fiddlesticks, Heimerdinger, Karma, Karthus, Lissandra, Lux, Malzahar, Morgana, Orianna, Swain, Taliyah, Veigar, Vel'Koz, Viktor, Zyra, Ziggs are all mages I find can do this with a moderate-to-exceptional degree of effectiveness, although there may be others who can do it with a certain playstyle.
tl;dr - Control Mage = Mage that uses utility to control the enemy's actions and make openings for someone to make a good play.