The relative static permittivity of a solvent is a relative measure of its chemical polarity. For example, water is very polar, and has a relative static permittivity of 80.10 at 20 °C while n-hexane is non-polar, and has a relative static permittivity of 1.89 at 20 °C. This information is important when designing separation, sample preparation and chromatography techniques in analytical chemistry.
The correlation should, however, be treated with caution. For instance, dichloromethane has a value of ε of 9.08 (20 °C) and is rather poorly soluble in water (13g/L or 9.8mL/L at 20 °C); at the same time, tetrahydrofuran has its ε = 7.52 at 22 °C, but it is completely miscible with water.  In the case of tetrahydrofuran, the oxygen atom can act as a hydrogen bond acceptor; whereas dichloromethane cannot form hydrogen bonds with water.
This is even more remarkable when comparing the ε values of acetic acid (6.2528) and that of iodoethane (7.6177). The large numerical value of ε is not surprising in the second case, as the iodine atom is easily polarizable; nevertheless, this does not imply that it is polar, too (electronic polarizability prevails over the orientational one in this case).