An Esper is an individual who holds psychic power derived from an energy they emit known as AIM controlled through their perception of themselves and the world, referred to as their Personal Reality, resulting in a power almost uniquely personal to each individual.
There are two kinds of Espers, of which you can decide to be one - Espers with scientific abilities such as Electrokinesis who make use of their powers through advanced mental calculations produced through Academy City's Power Development Program with standardized training and Gemstone Espers with esoteric powers such as being a living plant which are created naturally and need to learn how to use their power on their own.
There are several Levels of Espers, of which you start at Level 3 with either a power of your choice or one fitting you, which as a Level 3 is a strong, potentially multifaceted power convenient in everyday life.
You are guaranteed to be able to reach Level 5 through personal development and training, which holds power equivalent to a one-man army, but not Level 6, which can be considered the domain of God. Each level you advance will be exponentially harder to achieve.