In the most simplistic terms, Liam's power is telekinesis, the ability to move objects without coming into physical contact with them. Mind over matter.
Far more interesting, though, is Liam's true role in the book. Remember that "power" not only refers to his superhuman abilities but also the personal power that he has over the group and within himself. His real power is leadership. Great leaders seem to have a sort of charisma, an effortless attractiveness that entices others to follow them. It seems pretty clear that Liam's leadership ability is much like his telekinesis: innate, strong, and capable of "moving" people with without using force.
However, exerting power of any kind can result in horrible consequences and Liam's is no exception. The runaway children look to him for guidance. They trust him and that trust ultimately leads to the deaths of hundreds of kids when Liam's escape plan comes to fruition.
His other "power" is his willingness to accept and support Ruby, even though no one knows her full story or the extent of her power. In this capacity, he serves another important role of a leader: serving as a gatekeeper to the group. He's certainly attracted to her physically, and he senses her attraction to him, but he also, as we find out, understands Ruby on a level that even he cannot explain.