In the very-very end of the book, Alanna agrees to be Jonathan's squire, pledging her life to him. Then she takes a nap. Exciting, huh?
But if we backtrack a bit, we see that Alanna and Jonathan have just defeated the Ysandir (a.k.a. the Nameless Ones) against major odds. Jonathan finds out that Alanna is a girl during the fight, but he's not fazed: all he wants is an explanation of how and why she became a page. When Jonathan formally asks Alanna to be his squire, she swears loyalty to him and kisses "his hand, blinking back tears" (7.270). He responds, "by ruffling her hair" (7.271), reminding us that, even when they're king and page, Jonathan and Alanna are still just buddies.
Oh, sure she's still worried about Duke Roger possibly being a threat to Jonathan's safety, but that's a problem to deal with another day. Today, nap. As Alanna says, "If there were any more Ysandir about, she was too tired to care" (7.273). Fighting evil immortals sure takes it out of you, eh?
The significance of these ending tidbits is that Alanna has spent the whole book worrying that (1) people at the palace will find out she's a girl and hate her and send her home, (2) she won't be able to fight as well as a boy, and (3) she's unworthy of any honor or really anything good at all because she's a liar. But this ending puts all her fears to rest. Sure, not everyone knows her secret, but Jonathan is one of her best friends, and if he knows the truth and still accepts her, that's super-important to her. We get the sense that Alanna has grown and matured by the end of the book—not to mention that she's learned how to use a magic sword (among other things). She has friends who accept who she is. We'll take that over "and they lived happily ever after" any day.