The space around a body within which its gravitational force of attraction is experienced, is called its gravitational field.
Let M be the mass of a body around which a gravitational field exists. Let m be a test mass placed in this field. The test mass is so chosen that it does not influence the gravitational field. The arrow over indicates it is a vector quantity, whereas mass is a scalar quantity.
A force field is the force experienced by the unit mass m. The intensity of the field is the force experienced by the unit mass.
If the test mass m were free to move, it would move with an acceleration towards M.