Telekinesis is the ability to move objects with one's mind. This ability appears to be relatively instinctive, like when Stephen dropped his toothbrush. In the Tomorrow People telekinesis is based off a form of energy.
Telekinesis is an extremely versatile ability and can range from person to person as really weak to extremely powerful. The weakest being moving simple objects with your mind and the use of hand gestures, on the other hand as shown with the founder where he developed some sort of telekinetic shield without the use of any hand gestures and a split second to react. This prevented John from punching him and he tossed John around the room with ease.
Telekinesis can be used in ways such as levitating objects, or throwing people across a room, and finally stopping bullets fired from multiple machine guns. It can also used as a precision instrument, the way when Cassandra Smythe blasted a cement block to spell out "Hi Dad".
It has been shown that this type of telekinetic ability may be able to manipulate fire. The Citadel