The Eddington limit, or Eddington luminosity was first worked out by Arthur Eddington. It is a natural limit to the normal luminosity of stars. The state of balance is a hydrostatic equilibrium. When a star exceeds the Eddington limit, it loses mass with a very intense radiation-driven stellar wind from its outer layers.
Eddington's models treated a star as a sphere of gas held up against gravity by internal thermal pressure. Eddington showed that radiation pressure was necessary to prevent collapse of the sphere.
Most massive stars have luminosities far below the Eddington luminosity, so their winds are mostly driven by the less intense line absorption. The Eddington limit explains the observed luminosity of accreting black holes such as quasars.