I can understand what the electric field vector E and the magnetic flux density vector B mean, but what exactly are the meanings of the two other vectors, the electric displacement vector D and the magnetic intensity vector H? What are their physical explanations?
When mattter is present Maxwell's equations take on a more simple form when E is replaced by D and B replaced by H - a form similar to the vaccuum equations. The premitivity represents the polarization of the material and the permeability represents the magnitization of the material.
To elaborate a little:
Most types of matter have a tendency to align themselves with or against magnetic and electric fields in their vicinity, thus increasing or decreasing those fields. To a good approximation, you can often use D and H to represent the "imposed" or "external" fields, and E and B to be the real fields which will include the contributions from the matter.
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