Gravity is an archetypal example of a long-range force. The field strength in this case is defined as the force per unit mass that acts on a particle at any given point in the field. This is a sensible definition: It tells us how strong the gravity force field is by telling us the force that it exerts on an object of unit mass.
Gravitational field strength is a vector denoted by the symbol g. So, the definition tells us that
You will recognize this as being equivalent to the familiar formula for the gravitational force on an object of mass m:
So, the gravitational field strength is a vector with magnitude equal to the acceleration ...