A dielectric (or dielectric material) is an insulator that responds to an electric field, undergoing changes at the atomic and subatomic level termed polarization. The changes are the reposition of electrons, potentially entire atoms from the forces of the electric field, and the result is a strengthening of any "capacitor" response.
A capacitor, e.g., two separate electrically conductive pieces of something placed in an electric circuit, allows some current to effectively pass through, but resists more the more current enters until the current halts, a voltage forming that rises as current passes through until that situation. Placing the conductors close together, e.g., just a narrow insulator between them allows the attraction of the positive and negative sides to increase the amount of current allowed in, increasing the charges in the capacitor (its capacitance). If the insulator is a dielectric, the properties of the material increase the capacitance beyond what it would be otherwise.
Natural capacitors exist, e.g., clouds in electric storms, and astronomical bodies with magnetic fields and electric currents are affected by the dielectric properties of the body's constituents. Also, boundaries between material with different dielectric properties are what produces the reflections within bodies from ground-penetrating radar.