Relationship of Dielectric constant with ionic bond
You are probably referring to Coulomb's Law:

$${F\propto \frac{q_1 q_2}{d^2 \epsilon }}$$

This law, that you probably already met in physics, applies to chemistry and ionic bonds, since they are all characterized by electrostatic interactions.

You see that the strenght of a ionic bond is directly proportional to the product of the charges on the ions, inversely proportional to the square of their distance, and inversely proportional to the dielectric constant of the solvent. In vacuum, the dielectric constant is $\epsilon = 1$.

Otherwise, when the ions are in a solvent, the dielectric constant is associated to the solvent in use (you can find appropriate charts online).