Up to now, when have referred to `g` as the gravitational acceleration.  As anything released near the surface of the Earth drops with an acceleration of `g=9.8` m/s², this is certainly a correct characterization.  However, `\vec{g}` is actually telling up about a more fundamental quantity, the gravitational field.  Like the gravitational force, the gravitational field is a vector with a magnitude and a direction.  But unlike the gravitational force, which depends on an interaction between two masses, the gravitational field is an indication of how a single mass influences the space around it.  We talk about the gravitational force on a mass, but the gravitational field at a point in space.  How these two things relate to each other is explained by `\vec{F}_{g} = m \vec{g}`, which states that the gravitational force exerted on a particle sitting at a point in space is equal to the mass of the particle times the gravitational field at that point.