A Red Dwarf is a small star of Class M or late K - specifically a K V Star or M V Star. They are relatively cool in temperature, with a surface temp of no more than 3500 K, and less than half the size of our Sun. They are very dim stars, and difficult to see with the naked eye from earth. That said, they are the most common stars in our region of the galaxy - Proxima Centauri and twenty of the other 30 closest stars to our sun are Red Dwarfs. Red dwarfs produce heat energy via nuclear fusion of hydrogen into helium. They have slow, often stable reactions, and projected lifetimes in the trillions of years.
When finally that long lifespan is exhausted, the Red Dwarf will likely become a Blue dwarf (red dwarf stage), but it's believed that no such stars yet exist because the universe is not yet old enough. After blue dwarf, the progression goes white dwarf, then black dwarf - but it will be trillions of years before any of this can happen, and that's longer than the current life of the universe.
Red Dwarves emit very little ultraviolet light. Some are plagued by starspots that reduce luminosity by 40% for months at a time. Other Red Dwarves, known as flare stars experience gigantic flares (see solar flare) that doubles their brightness for several minutes at a time - such flares may result in coronal mass ejections that strip the atmosphere from nearby planets. Because they are cool and dim, the goldilocks zone is likely to be somewhat small - possibly small enough that otherwise habitable worlds would become Tide-Locked. The combination of these factors may make it difficult for (some?) Red Dwarf Stars to support life.
If so, that would be a shame, because the long lifespans of such stars would give plenty of time for life to evolve. Even if life doesn't evolve here, it's likely that eventually life will migrate to them. Stars like our own sun have a lifetime expressed in billions (not trillions) of years, and it's conceivable a society or species could evolve to have the technology needed to escape their own stars death and move outward. Such a society would no doubt have the tech to survive a few solar flares or starspots.