A dielectric is an insulating material in which all the electrons are tightly bound to the nucleus of the atom. There are no free electrons to carry current. Ebonite, mica and oil are few examples of dielectrics.
The electrons are not free to move under the influence of an external field. When dielectrics are located in an electric field, basically no current flows in them because, dissimilar metals, they have no heavily bound, or free, electrons that may drift through the material.