A quasar (from quasi-stellar radio object) is an astronomical object that looks like a star in optical telescopes (i.e. it is a point source), but has a very high redshift. The general consensus is that this high redshift is the result of the Hubble law and that their redshift indicates that they are very distant from Earth and that we observe them as they were several billions of years ago.
Since we can see them despite their distance, they must emit more energy than dozens of normal galaxies. Some quasars display rapid changes in luminosity, which implies that they are small (an object cannot change faster than the time it takes light to travel from one end to the other).
The first quasar was discovered in 1961 by Allen Rex Sandage at Mt Palomar, California. Once they were identified it was possible to find them recorded in photographic plates dating back to the 19th century.
Quasars appear to be a particular class of active galaxy nucleus, and a general concensus has emerged that what differentiates them from the other classes (blasars and Seyfert galaxies) is what angle we are viewing them at. The huge luminosity of quasars are believed to be powered by friction caused by gas and dust falling into supermassive black holes which can convert about half of the mass of an object into energy as compared to a few percent for fusion processes. This mechanism is also believed to explain why there are no nearby quasars, as this energy production ends when the supermassive black hole consumes all of the gas and dust near it.