A field in this context refers to any condition in which a force can be applied to an object over a distance with no physical contact. An every day example is gravity. The force of gravity acting on an object works over great distances of separation. The force created in this manner is dependant upon the "field strength". The field strength is measured at a test object located a distance from the object creating the field.
An electric field is created around any object which has an electric charge. The field strength is then measured by placing a test charge at a distance d away and determining the electrostatic force using Coulomb's Law:
Fe = kQq/d^2 where k is Coulomb's Constant, Q is the charge creating the electric field, q is the test charge, and d is the distance of separation. If we divide the force by the test charge we get
Fe/q =(kQq/d^2)/q. Leaving the quantity (kQ/d^2)
The (kQ/d^2) represents the electric field strength produced by the source charge and acting on the test charge at a distance of d.
Therefore, the quantity we get by dividing the force by the test charge is the electric field produced by the source charge.