The factor in which the capacitance of a capacitor is increased by using a certain dielectric as opposed to a vacuum. For example, if a capacitor with a vacuum dielectric had a capacitance of 1 farad, but if it uses another dielectric, and the capacitance rises to 5 farads, then the new dielectric that was used has a dielectric constant of 5.
Plastics tend to have dielectric constants of around 2 or 3. Glass, around 5. Mica has a constant of 7, and water has a quite high dielectric constant of 80.