Red dwarfs, or M-dwarfs, are the most common type of star as well as the smallest and dimmest main-sequence (hydrogen burning) stars. Because of their low luminosity and because many of them are fully convective and hence can burn a large fraction of their total hydrogen, they are very long lived, in many cases hundreds of times longer than our Sun. These trillion year lifetimes are much longer than the present age of the universe. Because they are so common, and because their small size makes it relatively easy to observe transits of their exoplanets, they are a favored place to look for Earthlike planets.
Such planets would have some funky properties. If they are in the habitable zone, the zone where temperatures permit liquid water to exist on planetary surfaces, they would be tidally locked to their star, keeping one face always toward it. Despite their dimness, red dwarf stars have a great deal of magnetic activity, and their titanic solar storms bombard their planets with a pretty intense flux of far UV radiation. This is likely to convert much of the CO2 in their atmospheres into oxygen and carbon monoxide.