Character Analysis
There are two important things about Yevaud and you already know both of them: a) Yevaud is a dragon, b) the dragon's name is Yevaud. (Did you follow all that?)
Yevaud is supposed to be an old, wise, powerful dragon, with eight children – that is, until Ged gets there, and he kills five or six of those kids, which is probably more than his dragon-hunting license allows. But when Ged names the dragon (as in, announces its true name), that's it for Yevaud – he must do what Ged asks of him. And that's how Ged saves the town of Low Torning from the dragons: he uses Yevaud's true name to make the dragons promise not to destroy all humans.
That's why Yevaud is here: although Ged has just (in Chapter 4) done something incredibly stupid and selfish – something that totally screws him up – in Chapter 5, he redeems himself a bit by doing something smart, selfless, and skilled. This selflessness is emphasized when Yevaud tempts Ged by saying that he can help the wizard fight the shadow. (Which would be an awesome grudge match.) Yevaud is primarily here to show us how Ged grows as a magician and as a person.
Also, Yevaud is here because what would a fantasy book be without a dragon? Actually, in the chapter with Yevaud we also do get a lot of information about the setting – about dragons and about the Old Speech. So we really do learn more about the fantasy world thanks to this dragon.