Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by defining a new physical quantity called the electric field.
In the new picture, imagine that the first charge sets up an electric field independent of all other charges in the universe. When another charge comes in its vicinity, the second charge experiences an electric force depending on the electric field at that point. The source charge does not exert any force on itself; however, all the other charges exert force on it.
The SI unit of the electric field is newton per coulomb. Since the electric field is a vector quantity, it is called a vector field. Since the Coulomb interaction follows the principle of superposition, by definition, so does the electric field.
It is to be noted that the electric field is defined by considering the test charge as a point charge. If the charge had a significant spatial extent, its different parts would experience different forces. In reality, since charges are quantized, and the fundamental unit is the charge of an electron or a proton, which are practically point charges, this is a good approximation.
The electric field is defined along the direction of the Coulomb force a positive charge would experience. Since a positive source charge would repel this positive test charge, the electric field of the positive point charge is directed away from it. On the other hand, the positive test charge would be attracted by a negative source charge; hence the electric field of the negative point charge is directed into it.
