A red dwarf is a small main sequence star, generally an M-type star
(M dwarf).
Sometimes the term is used to additionally include some or all main-sequence
K-type stars (K dwarfs), but K dwarfs can be referred to as orange dwarfs.
The red-dwarf mass range is from 0.075 to about 0.5 solar masses
and their surface temperature is 2000-4000 K.
Red dwarfs make up about 75% of the stars in the Milky Way,
and many of the nearest stars are red dwarfs.
Despite being so plentiful, they are so dim that none can be seen
with a telescope, including the closest star to the Sun,
which is a red dwarf.
They are of interest in the search for habitableextra-solar planets because there are so many, hosting many planets,
and the many nearby red dwarfs offer many planets for study, and the host's
relative dimness is conducive to direct imaging of the planets.
On the other hand, the red dwarfs can be quite active,
which can invade the habitable zone, which is close to the host star,
reducing the number of such planets that are truly habitable.
Red dwarf examples: