The maximum energy product is defined based on the magnetic hysteresis saturation loop (- curve), in the demagnetizing portion where the  and  fields are in opposition. It is defined as the maximal value of the product of  and  along this curve (actually, the maximum of the negative of the product, , since they have opposing signs):
Equivalently, it can be graphically defined as the area of the largest rectangle that can be drawn between the origin and the saturation demagnetization B-H curve (see figure).
The significance of  is that the volume of magnet necessary for any given application tends to be inversely proportional to . This is illustrated by considering a simple magnetic circuit containing a permanent magnet of volume  and an air gap of volume , connected to each other by a magnetic core. Suppose the goal is to reach a certain field strength  in the gap. In such a situation, the total magnetic energy in the gap (volume-integrated magnetic energy density) is directly equal to half the volume-integrated  in the magnet:
thus in order to achieve the desired magnetic field in the gap, the required volume of magnet can be minimized by maximizing  in the magnet. By choosing a magnetic material with a high , and also choosing the aspect ratio of the magnet so that its  is equal to , the required volume of magnet to achieve a target flux density in the air gap is minimized. This expression assumes that the permeability in the core that is connecting the magnetic material to the air gap is infinite, so unlike the equation might imply, you cannot get arbitrarily large flux density in the air gap by decreasing the gap distance. A real core will eventually saturate.