According to Halliday et al, the magnitude of Electric field is proportional to the number of lines per unit area perpendicular to the field.

My book (Halliday et al) states that this criterion, called Faraday's criterion, is helpful to draw field lines in a space region, but I can't understand why the area must be proportional to the electric field.
In my opinion, I think it is important because if the area is not perpendicular to the field, it is impossibile to collect all the field lines on the surface.
Then I want to know if this criterion is valid only if the magnitude of electric field is constant everywhere on the surface or not. 

If I assume there is an electric field in a space region with magnitude and direction which are not the same for each point, how do I apply this criterion?

I hope someone can help me. I feel discouraged by now and I would like to learn more.