Gauss's Law

Hey everyone,
I was wondering if someone could explain Gauss's law. For whatever reason, I just cannot grasp this idea (might be my teacher). I understand that the electric field through a surface can be represented as $\oint \vec{E} d\vec{A}$ but every problem that we do ends up resulting in it equaling $E\oint dA$ and finally EA. I really don't even understand this equation, how to use it, how to apply it, etc. If anyone could clear this up that'd be great.

Thanks.

guass law: the total flux through a surface is (1/$\epsilon$) times the total charge enclosed within it .. we take integral of E.ds to arrive to a equation ie $\phi$ = q/$\epsilon$ .