To understand what an electric field is, one must start with forces. Generally speaking, a force is anything which produces a push of a pull. Forces work in two general ways: by contact and at a distance.
Forces which work by contact are those which require the object creating the force to be in physical contact with the object to which it is applying the force. An common example would be if you were trying to push a car out of the mud. You would have to actually touch the car as you tried to push it.
Forces which work at a distance are those in which that which creates the force does not physically touch the object to which the force is being applied. A common examply would be gravity acting on a falling ball. The Earth creates the force due to gravity which makes the ball fall, but the Earth does not touch the ball while it is falling.
Forces which work at a distance alter the nature of space which surrounds them. When they are applying their force to another object it is actually the altered nature of space which is transferring the force. A field is the altered space. So, in our simple example, the Earth causes the ball to fall by creating a gravity field around the Earth and it is the gravity field which causes the ball to change.
Like gravity, electric forces also act at a distance. An electric charge alters the space around it in such a way that it can transfer an electric force to another electric charge without touching it.
An electric field is the region of space around an electrically charged object which transfers its electric force to other electrically charged objects.
The electric field is symbolized with E and is a vector. To determine the direction and strength of E one must know the size of the electric charge creating it, whether that charge is positive or negative, and how far from the source the field is being measured.
The general form of the equation for E created by a point charge is obtained from Coulomb's Law:
E = kQ/r^2
Where K is Coulomb's constant
Q is the size of the charge creating the field
And r is the distance from Q where the field strengh is measured.