While the stars the Disc passes by are balls of fire a mile across, and while the sun itself is even bigger, the Red Star is an astronomical object that dwarfs the entire Disc, combined with the World Elephants and Great A'Tuin. In fact, it's much more like the stars of the Roundworld universe.
Appearing during the events of The Light Fantastic, it is apparently the Destination of Great A'Tuin- or at least, the Destination up to the events of The Light Fantastic. As the Disc approaches it, the sky takes on a reddish color, and magic begins to fail. In fact, should the World Turtle draw too close, or remain there too long, magic would fail entirely and the Disc would be ripped off A'Tuin's back and be destroyed.
When the star first appears, only anthropomorphic personifications like Death (and possibly the gods and other higher beings) are aware of it. Death, when summoned by the Rite of AshkEnte, is forced to tell the wizards of Unseen University about the threat to the Disc, and also that the Octavo (and its eight spells) are needed to stop the Disc's destruction. The wizards immediately send out search parties to try and find Rincewind, whose mind is containing the eighth spell and whose body is somewhere in the forest of Skund, but fail because each Order is dedicated to stopping each other Order from claiming Rincewind first.
Eventually, as the star grows bigger and bigger and magic begins to fail, the cult of the Star People arises. Wizards are killed (as they lack the magic to defend themselves), books are burned, and non-human races (like the dwarfs) are attacked. A mob attempts to storm Unseen University, whose massive octiron gates are held together only by the failing magic and lacks any kind of fail-safe- like a big metal bar. The mob demands that the wizards stop messing around and get rid of the star, but this does not happen until after Archchancellor Ymper Trymon gets taken over by a beast from the Dungeon Dimensions and kills the rest of the senior wizards before he is stopped by Rincewind and Twoflower. After these events, Rincewind (with pronounciation help from Bethan and Twoflower) reads the eight spells of the Octavo.
This causes eight World Turtle eggs, incubating on the edge of the Red Star, to hatch (revealing baby turtles with young, molten discworlds on their backs), and A'Tuin to turn away and begin the journey away from the Red Star. For then it is revealed that the Red Star serves as a source of heat for the World Turtle eggs to incubate, while the World Turtle parents go elsewhere.
This fact seems to validate the Big Bang Hypothesis- except, it suggests A'Tuin has already mated with another World Turtle, raising all sorts of interesting questions. Perhaps this is why the fifth Elephant fell off?