The temperature has a definite value at every point in a room. Temperature at any point can be measured by putting thermometer at that point and the temperature distribution can be described either with a mathematical expression, say T(x,y,z) or by plotting the temperature variation on a graph. Such a distribution of temperature is called temperature field.
In the similar fashion the pressure can be measured at different points of a fluid and so obtain a representation of pressure field that describe the pressure in the space.
Such fields are called scalar fields since temperature and pressure are scalar quantities. If the temperature and pressure do not vary with time then they are called static fields otherwise they are time-varying fields. Time-varying fields are mathematically represented as V(x,y,z,t).
The velocity in a fluid can be represented by a field of flow associated with every point of the fluid. This is an example of a vector field. If the flow velocity remain constant with time then the velocity field is static and is represented by mathematical function V(x,y,z)
Gravitational field g is defined as gravitational force per unit test mass. This field is also vector field and is usually static when the distribution of mass of the gravitating body (i.e the source of the field) remains constant. Near the surface of the earth and at the points not too far apart it is also a uniform field meaning that g is the same in direction as well as magnitude for all the points.
Before the concept of fields was widely accepted. The force between the gravitating bodies was thought to be a direct and instantaneous interaction. This view, called action at a distance was also applied to electromagnetic forces. According to this view, the effect of the movement of one body is instantaneously transmitted to the other body. This view voilates the special theory of relativity which limits the speed at which such information can be transmitted to the speed of light. A more modern interpretation is that each mass interact not directly with another mass but instead with the gravitational field established by the other mass.
