Alia is Paul's sister and the daughter of Leto Atreides and the Lady Jessica. Since Alia was in the womb when Jessica consumed the Water of Life, she gains consciousness in utero as well as the Other Memory of the Fremen. The result? One scary little girl—like Japanese horror film scary.
Alia's mental prowess goes well beyond her tender young age. She speaks better than any child, understands the inside jokes of adults, can see into the future a bit, and is even able to kill her grandfather, the Baron Harkonnen, with the gom jabbar. Not bad for someone who's not even in pre-kindergarten (or whatever the Fremen equivalent is).
As a character, Alia's inclusion feels more like sequel setup than necessary role. She plays a much larger role in Dune Messiah and eventually becomes the main antagonist in Children of Dune. How does she go from being Paul's darling sister to a deadly antagonist? You'll just have to keep reading to find out.