The electric field is something that exists throughout all space, and only charges can interact with it.
The electric field is something used to help describe 'action at a distance'.
Imagine two charges separate from each other, both charges experience a force, however they are not touching. The electric field is needed to describe why they experience a force.
The electric field strength is defined as the force experienced per charge Q, sitting in that field.
E=F/Q
The electric flux can be seen much like a flux of water.
Here the flux (flow) of water is the amount of water passing through an area.
Just as with water, the electric flux is the amount of electric field passing through an area.
The stronger the electric field - the higher the flux, per unit area.
Imagine flux as a flow of the electric field.
Flux = E*A