The Bersallin sun was the primary of the Bersallis system. Fire storms on Bersallis III were generated by the particle emissions of this star. These emissions caused a cascade effect in the planet's atmosphere.
In 2369, Nella Daren mentioned the sun during a dinner with Jean-Luc Picard, but interrupted herself mid-sentence, fearing she was boring him. (TNG: "Lessons")
This star was only mentioned in dialogue.