Gravitational Potential (often symbolized by Φ) is a mathematical field (function on space dimensions) that indicates the strength of Gravity's effect on each point in space. It is the amount of energy required per unit mass to move the mass far away (e.g., infinite distance, approximated by a point very distant from any mass). I.e., the Gravitational Potential Energy per unit mass at each point. (An actual object at some point would have that point's gravitational potential times the object's mass as its gravitational potential energy.)
Gravitational potential's gradient (direction and magnitude of most rapid change over distance) is directly related to the acceleration imposed on something at that point, i.e., the force per unit mass. As such, it captures the specifics of a gravitational field as a scalar field, i.e., no direct reference to vectors or the direction of the force.
Gravitational potential is useful for Dynamics and Kinematics, such as orbital mechanics.