A red dwarf is a small M-type star (M dwarf). Sometimes the term is used to include K-type stars (K dwarfs), but sometimes those are referred to as orange dwarfs.
The mass range is from .075 to about .5 solar mass. The surface temperature is 2000K-4000K.
Red dwarfs make up about 75% of the stars in the Milky Way, and many of the nearest stars are red dwarfs. They have become of interest in the search for habitable extra-solar planets because there are so many (thus host many planets), so many are close (allowing planet study), and their relative dimness is conducive to direct imaging of the planets.
Red dwarf examples: AD Leonis, Barnard's Star, Lacaille 9352, Lalande 21185, LHS 1140, Ross 154, Ross 248, Scholz's Star, TRAPPIST-1, and Wolf 359.