Gravitational intensity is measured in units of acceleration, since as Galileo and Eotvos both showed, all objects have the same acceleration in the same field, irrespective of their mass.  So on the Earth's surface, its value is about 9.8 m/s^2.

A gravitational force of attraction exists between any two bodies that each have a mass greater than zero. This force exists no matter how great the distance between the bodies. The magnitude of the force can be determined using F = G(m1 x m2)/r^2 where G is the gravitational constant, m1 and m2 are the masses of the two bodies and r is the distance between them. To be accurate we consider the mass of each body to be concentrated at a point.

The effect of the force is to cause acceleration of the bodies towards each other. Acceleration is given by a = F/m.

If we were to consider m1 to be the mass of the earth (for example) the acceleration of any body with mass m2 towards the earth is given by G.m1/r^2.

Further examination (by reversing m1 and m2) will show you that although, if you jump off a bridge, you will accelerate towards the earth the earth will also accelerate towards you.

Because we are generally dealing with one very large mass and one very small mass it is easy to use acceleration as a measure of the attraction between two bodies.

The gravitational field, f, at a distance r from a body with mass M is given by f=GM/rr; it is thus stronger for a more massive body at the same distance away; and weaker for the same body at a greater distance away.

This field is 'what is there' due to M and is independant of externals.

Should a second body of mass m now heave into view, there will be an attractive gravitational force, F, between them; this is given by the product of the field due to the first, f, and the mass of the second, m.

ie F=mf =m(GM/rr) =GMm/rr

It follows that the field can thus be thought of as the 'force per unit mass'

There is a direct correlation with the field due to an electric charge, Q, given by f=Q/4(pi)(Eo)rr and the force, F, exerted upon a second charge, q, which is given by F=qf =q(Q/4(pi)(Eo)rr) =qQ/4(pi)(Eo)rr

Since a force, (gravitational or electric), can only exist between two objects, (masses or charges), the field can be thought of as 'that which is there, due to the first, when there is no second to act upon'