At the start of The Phantom Tollbooth, Milo is just a boy, a bored boy who's not satisfied by anything. When he's introduced to us at the beginning of the book, it seems like his most prominent characteristic is, in fact, being bored:
When he was in school he longed to be out, and when he was out he longed to be in. On the way he thought about coming home, and coming home he thought about going. Wherever he was he wished he were somewhere else, and when he got there he wondered why he'd bothered. Nothing really interested him – least of all the things that should have. (1.2)
It's like the grass is always greener on the other side for him: he's always dissatisfied. But Milo's not a bad kid: he just doesn't know any better than to be bored. Once he gets going, we – and he – discover that he's got a great sense of adventure.
Practically the first thing he does is the Lands Beyond is conquer his boredom, by seeing what happens to others when they're bored (the Lethargarians in the Doldrums). Milo very quickly realizes the danger of doing nothing, and he sees the effects of this in the Lethargarians, even though he couldn't see it in himself. Lesson learned. But wait, there's more.
Curious, brave, honorable: Milo's got everything necessary to be a good explorer. He's happy to go new places and try new things. Think about it: as soon as he finds out that Rhyme and Reason have been banished, he becomes determined to rescue them. This means going to places he's never seen and encountering people he's never met. Even worse, it involves risking his life and being brave enough to stand up to demons. But he doesn't hesitate. Milo just keeps going and explores the Lands Beyond for all they're worth.
Even though he makes a few mistakes – think about his speech at the banquet or his failed attempt at conducting the orchestra – Milo is super smart. Even though he keeps encountering unfamiliar concepts (like different points of view, the dangerous power of words, and the stretchy qualities of infinity), Milo is able to outsmart one of the smartest people in all of the Lands Beyond, the Mathemagician:
"Then each of you agrees that he will disagree with whatever each of you agrees with," said Milo triumphantly; "and if you both disagree with the same thing, then aren't you really in agreement?"
"I'VE BEEN TRICKED!" cried the Mathemagician helplessly, for no matter how he figured, it still came out just that way. (16.56-57)
Milo is sure to cross all his T's and dot all his I's: he doesn't leave anything out during his quest, and in the end, it pays off. He's rewarded with gifts from both the king and the Mathemagician – as well as gifts from Alec Bing and the Soundkeeper – that enable him to succeed against all the demons he encounters. Take that, demons.
By the end of the story, Milo has been cured him of his boredom for good: "'Well, I would like to make another trip,' he said, jumping to his feet; 'but I really don't know when I'll have the time. There's just so much to do right here'" (20.19). He doesn't need the tollbooth to have adventures, so he's able to make a go of it on his own. Talk about a transformation.
Some readers may criticize Milo as being kind of a blank character. And in fact, so might the author. In an interview with Adam Gopnik, Norton Juster even admitted that "he was actually concerned, when he was halfway through writing the book, that Milo would seem too empty" (source). It's true that it might be harder to come up with a mental picture of Milo than one of Jane Eyre or David Copperfield. But maybe it's a good thing that Milo doesn't have tons of personality quirks and isn't described in an extremely specific way. If he is a little "empty," there's nothing keeping us readers from identifying with him. And by identifying with Milo, we can go with him more completely on his journey.
See, Milo is like our tollbooth. We use him as our gateway to the Lands Beyond in the same way he uses the tollbooth as his. We can't get to these Lands unless we go there with Milo. We hitch a ride on his way to discovery. Although he doesn't realize it, Milo is our guide. We have the opportunity to learn all these interesting things about words and numbers, sights and sounds – and most importantly, imagination – just as he does. Whether we take it in is up to us.