I understand the physical meaning of electrostatic energy of a system of charges (or a distribution with given density) as the energy stored in the system while working to carry the charges from infinity to their actual place in the system. According to [this](http://en.wikipedia.org/wiki/Electric_energy) article on Wikipedia, in the case of a static field you can also compute that energy as the integral of energy density $U=\int\frac{1}{2}\epsilon\_{0}|\vec{E}|^2dV$. What is the physical interpretation of this density? What is the physical meaning of the expression *energy of an electrostatic field* and can this concept be used also in the non-static case? And with other fields as the gravitational one?

P.S. I hope this question doesn't seem obvious or useless. Being a student of mathematics, I really like to think about an abstract field $\vec{E}$ governed by Maxwell equations and *then* give it some physical meaning, unfortunatly I have not seen any theoretical physics yet, only some general physics.