We know that the neutron is electrically neutral to better than one part in 10²¹. But we also know that neutrons are made up electrically charged sub-units called quarks.   Furthermore we know that the neutron charge distribution has a radial dependence.   But as far as we know the charge distribution is spherically symmetric. A non-zero electric dipole moment would contradict that, it would mean that neutrons are not quite round. Imagine a neutron the size of the earth. At that scale the nEDM@SNS goal precision (d_n < 3×10^-28 e·cm) can be translated into a relative difference between the polar and equatorial diameters that is a mere tens of nanometers.