Question

What do you mean by displacement vector D ?

Answer 1

The electric displacement vector $\mathbf{D}$ in a dielectric material is defined as

$$\mathbf{D} \equiv \varepsilon_{0} \mathbf{E} + \mathbf{P}$$

where $\varepsilon_{0}$ is the vacuum permittivity, $\mathbf{E}$ is the applied electric field, and $\mathbf{P}$ is the polarization density - density of the permanent and induced electric dipole moments in the material.

According to the Maxwell's equations, the flux lines of $\mathbf{D}$ must begin and end on the free charges. Thus, it can be considered as sort of analogue of electric field of free charges in a dielectric material (but only sort of, the exact definition is given by the expression above).