An electric field (conventionally termed E in equations) is the tendency at each point in space to force an electrically-charged object in a particular direction, per Coulomb's law. Mathematically, it is a gradient, a function on the three dimensions of space yielding a vector in a direction along the line of the force (which pushes objects of the two polarities in opposite directions along the line) with a magnitude consisting of the amount of force applied to an object at that point per unit mass and unit electric charge of the object. This field is the gradient of a mathematical field, which is termed the field of electric potential.
Two possible mathematical fields describe such a physical field, so by convention, the field is such that the vectors point in the direction that a positively-charged object is pushed. (The other possible mathematical field would just have all the vectors in exactly the opposite direction, showing the direction that a negatively-charged object would be pushed.)
An electric field is analogous to a gravitational field, both following inverse square laws, but incorporates the concept of electric charge with a polarity (positive and negative) and that each polarity attracts the other polarity but repels objects with the same polarity.