Where The Kings and Queens of Old (Peter, Susan, Edmund, and Lucy) live, along with Caspian. They are the rulers of Narnia and all that.
"The Narnia books say nothing about when Cair Paravel was built or by whom. The first King and Queen were Frank and Helen (both came from the world of men), but we are not told where they lived in Narnia. Their coronation took place at Lantern Waste, far from Cair Paravel. Their children became the first kings and queens of Narnia and Archenland. See The Magician's Nephew and The Horse and His Boy. Cair Paravel is first mentioned in the book The Lion, the Witch and the Wardrobe. It already exists at that time. Among the titles claimed by Jadis, the White Witch is that of 'Chatelaine of Cair Paravel'. Though not dwelling there she keeps it maintained in a good condition. The subversive prophesy current among inhabitants of Narnia is that eventually 'Two Sons of Adam and two Daughters of Eve' would be enthroned at Cair Paravel. This implies that it had already been a royal seat, though this is not explicitly stated. When the four Pevensie children (Peter, Susan, Edmund, Lucy) become Kings and Queens of the country after the defeat of Jadis, Cair Paravel becomes the seat of the court of the Pevensie children and the capital of Narnia. In the book Prince Caspian, which takes place many centuries of Narnian time after The Lion, the Witch and the Wardrobe (but only a year in our time), Cair Paravel is a ruin on an island at the point where the Great River of Narnia flows into the Eastern Ocean. It is here that the four Pevensies return to Narnia, although it takes them a while to realize where they are. In The Silver Chair it is told that Caspian X the Seafarer had rebuilt the castle by the end of his reign. In The Last Battle Cair Paravel is surrounded by a city and is eventually captured by a surprise sea-borne attack by and sacked by troops of the Tisroc of Calormen, last mentioned as being 'full of dead Narnians and living Calormenes'. Cair Paravel is later destroyed along with the rest of Narnia, but has its counterpart in the "Real Narnia" to which protagonists arrive."
-Sourced from the Wikipedia Archives of Xyzzy Library