Originally a term coined by Michael Faraday to provide an intuitive paradigm, but theoretical construct (in the Kuhnian sense), for the behavior of electromagnetic fields, the term force field refers to the lines of force one object (the "source object") exerts on another object or a collection of other objects. An object might be a mass particle or an electric or magnetic charge, for example. The lines do not have to be straight, in the Euclidean geometry case, but may be curved. Faraday called these theoretical connections between objects lines of force because the objects are most directly connected to the source object along this line.
A conservative force field is a special kind of vector field that can be represented as the gradient of a potential.
Note that a force field does not exist in reality, per se, but it is really a Kuhnian construct that allows scientists to visualize the effects of objects on other objects; in other words, it makes the math easy.
In science fiction and fantasy literature, a force field or protective shield is a barrier made up of energy to protect a person, area or object from attacks or intrusions. The idea may be based partly on the concept of a vector field, though in character it resembles the "warding spells," the defensive magic claimed to be used by the Druids and shamans of the ancient world.