The basic physics concept we are currently working with is that electric charges create a disturbance in the electric field that permeates space (and that will cause electric forces on other charges moving in that field).
The idea of Gauss' Law is to look at some region of space, define an abstract surface in that space and calculate something called the electric flux. This will measure how much electric field goes through that surface. This should then allow us to determine the amount of charge inside the surface.
We will define electric flux as electric field times the area but the direction of the surface will matter. We will therefore define a vector for the area to be
The electric flux is then (for a constant electric field over the surface)