Art © Angelo Nero.
A white hole is the opposite of a black hole; more precisely, a black hole that runs backward in time. The concept of a white hole comes about because the Schwarzschild geometry of a black hole allows a negative square root as well as a positive square root solution. The negative square root solution corresponds to a white hole. The complete geometry then consists of a black hole, a white hole, and two universes connected at their horizons by a wormhole.
Just as a black hole irretrievably swallows everything that falls into it, a white hole only spits energy and matter out. However, because white holes appear to violate the second law of thermodynamics it seems unlikely that they exist in nature. There was some early speculation that quasars might be white holes; however, this has now been discounted.