"Quasi-stellar objects" (or QSO's) are defined observationally as
objects that appear star-like on photographic plates but have high
redshifts (and thus appear extragalactic; see above).  The luminosity
(if we accept that the redshift correctly indicates the distance) of a
QSO is much larger than that of a normal galaxy, and many QSO's vary on
time scales as short as days, suggesting that they may be no more than a
few light days in size.  QSO spectra typically contain strong emission
lines, both broad and narrow, so that the redshift can be very well
determined.  In a few cases, a nebulosity reminiscent of stars in a
normal galaxy has been detected around a QSO.  Quasars (a shortened
version of "quasi-stellar radio source") were originally discovered as
the optical counterparts to radio sources, but the vast majority of
QSO's now known are radio-quiet.  Some authors reserve the term "quasar"
for the radio-loud class and use the term "QSO" generically; others
(especially in the popular literature) use "quasar" generically.

In the standard model, QSO's are assumed to lie at the centre of
galaxies, and to form the most extreme example of the class of active
galactic nuclei (AGN); these are compact regions in the centre of
galaxies which emit substantially more radiation in most parts of the
spectrum than would be expected from starlight.  From the energy
output in QSO's, together with some guess at their lifetime (about
10^8 years) the mass of the central engine can be estimated as of
order 10^7 solar masses or more (this is consistent with estimates of
the masses of other, related types of AGN).  A compact, massive object
of this kind is most likely (on our current understanding of physics)
to be a black hole, and most astronomers would accept this as the
standard assumption.  The luminosity ultimately derives from matter
falling into the black hole and gravitational potential energy being
converted to other forms, but the details are unexplained and very
much an active research topic.