Dielectric materials are insulators that can be polarized in the presence of an electric field. Without an electric field, the polar molecules of the dielectric are oriented in random directions. An applied electric field causes the molecules to reorient uniformly since the negative and positive ends of each molecule in the dielectric are attracted to the positive and negative sources of the field, respectively. This is illustrated in Figure 1, which shows the uniform orientation of some molecules.
Dielectrics are commonly found in circuits, primarily in capacitors. The polarization of the dielectric creates an electric field within it that acts in the opposite direction of the field created by the charged plates of the capacitor. This reduces the magnitude of the effective electric field between the charged plates, which increases the capacitance of the capacitor. Therefore, higher voltages can be applied to the capacitor without reaching its maximum capacity. This also means that the dielectric must be a strong insulator in order to prevent any current leakage between the plates.
For more information on dielectrics, see HyperPhysics.