An electric field (conventionally termed E in equations) is a physical field that at any point, applies some force to any electrically-charged object located that point 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. The field that it is the gradient of 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 possibility would 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.