Concilium (also known as Coercion or Mind Control) is the ability to control another's mind through sheer willpower, allowing the one performing concilium to control their actions, memories, thoughts, etc. It is one of the Seven Wonders (meaning all Supremes are expected to have mastered over this ability) and it is the most often used ability, after Telekinesis.
Similarly to witches, even beings afflicted by an unknown blood virus have proved to be skilled in various degrees of mind compulsion. However, vampiric abilities have never been classified and explained as happened to witches' powers.
Concilium is the art of imposing one's will into another. Myrtle Snow stated that the sharper a person's mind, the more effort it takes to control them, but a person skilled in Concilium can break any mind. It is possible to try and resist it, shown when Fiona Goode tried to hypnotize a police officer and he refused, but it can lead to a build-up of extreme pain in the brain and can be fatal. It also can control their thoughts, memories, and feelings. 
Fiona showed Madison Montgomery how to perform it when she became her protege. Madison managed to hypnotize a man into standing in the middle of a road.  She was later shown to be very skilled in the ability during the Trial of Concilium.
Nan was also shown to have developed Concilium, when she very nearly forced Madison to stick a cigarette up her vagina, and when she later murdered Joan Ramsey by hypnotizing her into drinking bleach. 
The young candidate for Supreme during the Seven Wonders skit was able to make another witch walk around like a chicken. 
At the Trial of Concilium, two people stood opposite each other and each was given the chance to control the other. Misty and Queenie were partnered up, with Misty making Queenie slap herself several times and Queenie forcing Misty to pull her hair. Zoe and Madison were much more violent. Madison first forced Kyle to drop his tray of wine glasses, to anger Zoe, and then forced him to kiss her whilst making Zoe slap herself, then forcing Kyle to lick her boot whilst Zoe watched. In return, Zoe forced Kyle to break free from Madison's control and kiss Zoe, but out of anger, Madison forced Kyle to choke Zoe. The fight was ended when Cordelia telekinetically threw Kyle across the room. Cordelia, during her own test, made Queenie perform a tap dancing routine much to everyone's laughter.