The Eddington limit, also called the Eddington luminosity, is the point at which the luminosity emitted by a star or active galaxy is so extreme that it starts blowing off the outer layers of the object. Physically speaking, it is the greatest luminosity that can pass through a gas in Hydrostatic equilibrium, meaning that greater luminosities destroy the equilibrium. Hydrostatic equilibrium is the quality that keeps a star round and approximately the same size over time.
The theoretical limit at which the photon pressure would exceed the gravitational attraction of a light-emitting body. That is, a body emitting radiation at greater than the Eddington limit would break up from its own photon pressure.
Source: wikipedia, NASA