Quasars are very distant objects in space. They are relatively small objects that can be as bright as an entire galaxy. They are among the brightest objects in the universe.
They may be centers of some distant galaxies, surrounding a supermassive black hole. The tremendous energy that makes them so bright is believed to be supplied by the black holes in the centers.
They were discovered through telescopes as objects with a very high red-shift. By the standard definition of a red-shift, it means these objects are moving away from us at extremely high speeds.
Including image: http://en.wikipedia.org/wiki/Quasar