Eddington luminosity (sometimes also called the Eddington limit) is the largest luminosity that can pass through a layer of gas in hydrostatic equilibrium, supposing spherical symmetry. If the luminosity of a star exceeds the Eddington luminosity of a layer on the stellar surface, the gas layer is ejected from the star.
The exact value of Eddington luminosity depends on the mass of the star and chemical composition of the gas layer. A rough estimate is 33000 solar luminosities per solar mass.
Gamma ray bursts, Novae and supernovae are examples of systems exceeding their Eddington luminosity by a large factor for very short times. In those cases, the result is a radical change in physical structure (namely, the ejection of a fraction of the star's mass).
Some X-ray binaries and Active galactic nuclei are able to maintain luminosities close to the Eddington limit for very long times.