The electric potential measures the potential energy possessed by a charge per unit charge itself: it is a scalar quantity that summarises in a single number, point by point, all the information contained in the electric field. Knowing everywhere is equivalent to knowing : the field is obtained from the potential via the gradient, and the potential is obtained from the field via the line integral.
These atoms develop the notion of potential starting from its energetic definition, show how to invert the link to obtain the field, and establish the fundamental property that makes the electrostatic field conservative.