For most of the book, Rannulf reminds us of Aragorn in The Fellowship of the Ring, sitting in a dark corner with a hood over his eyes as everyone wonders who the heck this guy is.
Part of his mystique comes from the fact that, as a non-English Muslim, the English regard him as a barbarian: "I could imagine Rannulf watching bears consume either one of us, out of interest in the way the bears used their claws" (9.37). It is kind of racist? Yup. But no one ever said the Crusaders were perfect.
On the upside (in terms of his depiction in the book), Rannulf looks way scarier than he is: "The scar above Rannulf's mouth gave him a permanent sneering look, but his gaze was not unfriendly" (8.37). And he confides in Edmund that people are way too quick to judge the book by the cover: "'Men misjudge me,' he said peacefully. 'Inside, I sing songs like the ones Miles used to love, and I offer Heaven my own sort of prayers'" (25.24). We're all human underneath it all, yo.
Rannulf's an important guy because he bridges the gap between the Christians of the West and the Muslims of the East. At first, Edmund's surprised that he's part of the group. He says, "I thought Christians were forbidden to speak to a man like Rannulf" (7.10). Yeah, the world they live in draws really solid lines between people based on their homeland and systems of belief (for more on this, swing by the Themes section and read up on "Religion" and "Foreignness and 'The Other'").
But though Rannulf doesn't follow the same letters of the law, it turns out that he has more in common with the English than they think. This really hits Edmund when he hears the knight invoke God: "God's strength. It was a phrase Father Joseph used, encouraging my father as he faced death. Perhaps, I thought, Rannulf is not such a prayerless man after all" (8.44). Perhaps he isn't, Edmund, and good on you for rethinking your opinion.
Rannulf is also a mentor to Edmund. He's not as blunt and outspoken as Nigel, so he nurtures young Edmund like sunlight helps a flower grow. And he helps Edmund build confidence. For example, when Edmund tries to apologize for being sick with fever, Rannulf calls him out: "A squire with a strong arm who can read a ship's chart—at what exactly are you useless, Edmund?" (21.17). It's a much-needed boost from a man who challenges much that Edmund takes for granted about the world.