A quasar (from quasi-stellar radio source) 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 cosmological, the result of Hubble's law and that their redshift indicates that they are typically very distant from Earth; 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 highest redshift quasar currently known is 6.4 ([1]).
The first quasars were discovered with radio telescopes in the late 1950s; the first spectrum of a quasar, confirming its extragalactic nature, was obtained by Schmidt in 1963. Once they were identified it was possible to find them recorded in photographic plates dating back to the 19th century. Later it was found that not all (actually only 10% or so) quasars have strong radio emission (are `radio-loud'). The name `QSO' (quasi-stellar object) is sometimes given to the radio-quiet class. Other people talk about `radio-loud' and `radio-quiet quasars'.
Quasars appear to be a particular class of active galaxies, and a general consensus has emerged that in many cases it is simply the viewing angle that distinguishes them from other classes, such as (blazars and radio galaxies). The huge luminosity of quasars is believed to be a result of friction caused by gas and dust falling into the accretion disks of supermassive black holes, which can convert about half of the mass of an object into energy as compared to a few percent for nuclear fusion processes. This mechanism is also believed to explain why quasars were more common in the early universe, as this energy production ends when the supermassive black hole consumes all of the gas and dust near it. This means that it is likely that there are quiescent quasars in or near our local galactic neighborhood, which lack a supply of matter to feed into their central black holes to generate radiation.