Roughly speaking, this happens because of the coexistence and interaction of several subsystems within the substance (e.g., ferromagnetic and ferroelectric). For example, due to magnetostriction the magnetization leads to a change of the dimensions (appearance of distortion and stress), and this, in turn, leads to a change of electrical properties through the mechanism of electrostriction. And Vice versa
See also: Review Article "Modeling of Magnetoelectric Interaction in Magnetostrictive-Piezoelectric Composites" by M. I. Bichurin and V. M. Petrov in Advances in Condensed Matter Physics Volume 2012 (2012), Article ID 798310, 12 pages, http://dx.doi.org/10.1155/2012/798310
In a recent work I have shown that the photon as a quantum particle gives rise to additional term in Maxwell equations that express such an effect "magnetoelectric effect".