E is electric field intensity. D is electric flux density, aka electric displacement. If an E field is present in a dielectric, then the external source of E field reduced to zero, the dielectric will retain a state of polarization, called "D". Energy is stored in the dielectric.
A similar scenario takes place with ferromagnetic material. H is the magnetic field intensity. When H is reduced to zero, the ferrous material retains magnetic polarization & energy. The magnetic flux density is "B".
A good e/m fields text goes into detail with the math. I recommend peer-reviewed textbooks, & university web sites. Avoid web sites not peer reviewed. Many of these sites are kept by people who are just pretenders, want to be's, hackers, & know-nothings, seeking an audience. They will only confuse you.
Claude