For someone who is more of a mathematician than physicist, the following article might be of interest in this context: http://math.ucr.edu/home/baez/quantum/node4.html The gist is that the state space of a multicomponent quantum mechanical system (think electrons in a metal) is given by the tensor product of the single component state spaces. As might be familiar from linear algebra, not every element in the tensor product of two vector spaces is simply a tensor product of two vectors. That's really all there is to entanglement, but unfortunately you can't explain that to a lay person.