Telekinesis (from Greek: τηλε- "far off" and κίνηση "movement") is the ability to influence/control/manipulate matter or another aspect of a physical system with the ‘mind’ or through other non-physical means.
Commonly, the most basic and fundamental trait is to move or otherwise interact with objects (or alternatively, to generate and apply physical force on a target) both from a distance and without physical contact. As the ability is connected to the mind of the user, it can either be activated and controlled through conscious effort and concentration, through willpower and emotions of a particular level of intensity, through achieving a state of discipline and serenity, or simply through the whim and desire of the user. Moreover, these aspects of the user's mind and mental capacity at large can affect the capabilities and efficacy of their power, as well as its limitations. Telekinesis is one of the bases of many superpowers that are based on "controlling/manipulating," and may evolve to the point that a Telekinetic can control anything at a subatomic, particle, and universal level.
Through manipulating sound waves, Vanya can move and control objects, as well as generate force, with her mind. Offensively, she is able to immobilize, restrain, constrict and repel others with her energy. As a child, an irritated Vanya would cause several nannies to be sent flying across the room or, out of a window or down a staircase. When confronting Leonard, she projected and manipulated the sound waves around him, levitating him above the ground, holding him in a crushing grip and proceeding to telekinetically move various objects in the kitchen to impale him. As Pogo confirmed that he knew of her power and allowed her memory of it being erased, she proceeded to raise him into the air and hurl him across the Umbrella Academy living room and into the antlers of a mounted deer head. After her mind wipe due to time traveling back to 1963, she managed to empty an entire pond by causing the water to rise into the air, to the point where she managed to keep it suspended there while not actively focused on it, giving her more than enough time to carry Harlan from the pond and onto dry land before the water fell back down. When angered by an FBI interrogator in 1963, her powers activated and began to nearly choke him.
After having Vanya remove her powers from him, Harlan is shown to retain telekinetic abilities, effortlessly spinning a toy above his hand. This appeared to be connected to his former ability of absorbing and manipulating sound, due to the same resonating sound produced from both powers.