A flare star was a type of star which regularly experienced brief, random outbursts of solar flares over its surface disrupting energy patterns in its system and sometimes endangering lifeforms.
In 2365 the flare star Bringloid entered a period of intense activity, forcing the re-location of the Bringloid V colony. (TNG: "Up The Long Ladder")
Another known example of a flare star located within Federation space was Wolf 359. (TNG: "The Best of Both Worlds, Part II")