Why does Belle mean in this part in "A Change in Me"

Question

In the musical Beauty and the Beast (composed by the legend Alan Menken himself), Belle sings the song "A Change in Me" after she returns to her father when the Beast lets her go. She tells (or rather sings) to her father,

And I - I never thought I'd leave behind
My childhood dreams
But I don't mind
For now I love the world I see
No change of heart
A change in me

For in my dark despair
I slowly understood
My perfect world out there
Had disappeared for good

But in its place I feel
A truer life begin
And it's so good and real
It must come from within

What does Belle mean in this passage? What childhood dream did she love behind? What did she not love about the world she saw before? What's the perfect world that disappeared? What truer life? What does she mean?

Answer 1

In the early Act I song “Belle” she complained about the monotony of small-town life:

Little town, it’s a quiet village
Every day like the one before […]
Every morning just the same
Since the morning that we came
To this poor provincial town […]
There must be more than this provincial life!

and in “Belle (reprise)” she described her dreams:

I want much more than this provincial life!
I want adventure in the great wide somewhere
I want it more than I can tell
And for once it might be grand
To have someone understand
I want so much more than they’ve got planned

So these are her “childhood dreams”—to escape from the provinces, have adventures, travel places, and have people understand her ambitions.

But by “A Change in Me” (late in Act II), she realises that if she marries the Beast she is going to have to stay in the provinces, and will never have the “perfect world” she imagined for herself in Paris or wherever. But she is happy with this because she loves him, and so feels that this will be the “truer life”.