DOROTHY: Oh Hunk, you just won't listen, that's all.
"This mean old lady wants to kill my dog, and I could use a little assist from the grown-ups here." Sounds reasonable. Unfortunately, no one listens to her: which means that home is feeling pretty un-homey these days.
DOROTHY: Someday I'll wish upon a star and wake up where the clouds are far behind me.
Where troubles melt like lemon drops, away up on the chimney tops. That's where you'll find me.
Dorothy expresses the traditional hero's longing to get away from her futzy old home, which pretty much sets the whole plot in motion. It's interesting to note that home is initially somewhere to escape from, then becomes somewhere she'll do anything to get back to—all without changing in any way, shape or form.
DOROTHY: I had the measles once. She sat right by me every minute.
This is actually the first time we hear that Aunt Em might be something other than a sour-faced old killjoy. It's also important to recognize that Dorothy took a picture of Em with her, meaning that her heart really belongs at home even when she feels forced to run away.
PROFESSOR MARVEL: Poor little kid, I hope she gets home okay!
It's good to know that Professor Marvel, and by extension the Wizard, sympathizes with Dorothy's quest. Marvel, of course, lives in a traveling wagon, so he may know more than anyone else what it means to not have a home.
MAYOR OF MUNCHKIN CITY: I welcome you most regally…
The Munchkins may be sweet, but they're no good in a crisis. They heap Dorothy with honors and accolades, only to run for the hills when Wicked Witch 2.0 shows up. Maybe this isn't home either. They certainly don't protect her in any tangible way, even though they seem to acknowledge her in a way that she feels Auntie Em doesn't. It's every girl's wish to be seen as special.
DOROTHY: And it's funny, but I feel as if I'd known you all the time, but I couldn't have, could I?
This is an interesting line because it links Dorothy's buddies back to the farmhands at home in Kansas. Could it mean that Dorothy always has a little bit of home with her as long as her friends are at her side?
DOROTHY: I'm here in Oz, Auntie Em! I'm locked in the witch's castle, and I'm trying to get home to you, Auntie Em!
A heart-wrenching moment here. When times are bleakest, Dorothy still looks towards home. It's not only the object of her quest; it's the thing that gives her strength to carry on. It's a bit of a paradox, but it also explains why she wants to get back there so badly: it gives her comfort, even when Wicked Witches are trying to settle her hash.
WIZARD: I'm an old Kansas man myself.
This is the first concrete link between Oz and home for Dorothy, and also a connection between the Wizard and Professor Marvel. And just like home itself, the Wizard seems grim and a little scary at first, but becomes kindly and welcoming once Dorothy's quest is nearing an end. It's comforting when he says he's from Kansas; home seems a little nearer now.
DOROTHY: Auntie Em must have stopped wondering what happened to me by now. Oh, Scarecrow, what am I gonna do?
Notice that Dorothy's thoughts of home aren't selfish here. She's worried about Aunt Em, and about making sure her family doesn't worry about her. That makes her journey an especially heroic one: she's not just looking out for number one.
DOROTHY: Oh, but anyway, Toto, we're home. Home! And this is my room, and you're all here. And I'm not gonna leave here ever, ever again, because I love you all, and oh, Auntie Em there's no place like home!
These are the last lines of the film, so you know how much home means to our plucky young heroine. She expresses her joy at arriving safe and sound and seeing all the people who love her. It's that sense of love and safety that home represents: the place that when you go there, they have to take you in. (Props to Robert Frost)