The Faber-Jackson relation (FJR) is a relation between the luminosity of an elliptical galaxy and its central stellar velocity dispersion. It is something like a "Tully-Fisher relation for elliptical galaxies". It serves as a method of estimating the distance to a galaxy because the velocity dispersion can be derived from spectrography, by observing the effects of redshift and blue shift on spectral lines of the stars, yielding an absolute magnitude of the galaxy, which with the apparent magnitude yields an estimate of the distance, albeit a loose one.
A more recently-observed, useful relation, the D-σ relation, is between the diameter of an elliptical galaxy and its velocity dispersion. The fundamental plane is an even later development: a relation between radius, velocity dispersion, and surface brightness, which may yield an even better distance estimate through use of an additional observable.