The definition of power is the ability to do or act (note that words give us the power to define 'power' in the first place).
Words have the power to produce action in several ways. They can create emotions, moods, and levels of motivation, and can will people to action when they otherwise have sat complacent. They have the power to uplift and improve people's outlook on life, and the power to produce an environment of hate and fear. They can instruct people on a previously vexing problem, and enable people to communicate thoughts that would have otherwise been trapped in the mind of only one person.
Words fulfill the definition of power because they have the ability to create and influence real action.