i can honestly go on, and on about how much i love the one day i’ll fly away sequence and how it is both hauntingly beautiful and heartbreaking at the same time.

it gives insight to satine's feelings, about what she wants and how she hopes to find a way to make it all come true for her despite the life she's lived. a few scenes earlier while she's getting ready and dressed up to (supposedly) meet the duke with marie's help, we see satine tell her this:

and she proceeds to look at the bird locked in the cage when she exclaims that one day she would "fly away, fly away from here!" and she's filled with hope and excitement that one way or another it would eventually happen.

by the time we get to the actual part where the song is heavily focused and featured (which in my case is like her equivalent of part of your world, an 'I Want!' anthem) we see how through and through satine sings what she feels: i follow the night / can't stand the light -> this may pertain to being a 'creature of the underworld', since at the start of the film the moulin rouge was described as a 'kingdom of night time pleasures' and the imagery of her being in the shadows that i think symbolises her place in life as a dancer/courtesan/entertainer but truly wants to fulfill her dream as an actress before she takes her steps and we get to fully see her in the light right when we get 'when will i begin to live again'

an interesting note is when she sings the 'leave all this to yesterday' line, it pans right through the chains of the elephant zooming into the windmill and christian's garret. we see christian and satine seemingly glance back and forth at each other (?) from afar throughout this scene, which is fairly more obvious once we get to 'what would your love do for me / when will love be through with me?' like she was singing to him, we can see that she's also looking at him there though perhaps I guess she was just thinking out loud and not completely directly asking him these thoughts, and instead wondering to herself if she should let him into her life and what he could bring to it, and maybe he can be part of her dream to 'fly away.'

once she reaches the top of the elephant, it feels like a relief when she belts out 'one day I'll fly away!' for satine and the audience watching. you feel her need and want to leave this place for something better, and to chase what she was always dreaming of and it shows how constraining it was for her to have just been there for years and years, she screams to the world how she wants to fly away and be free and allow herself to follow her heart.

later on towards the latter part of the movie, we get a reprise of this song right after the moment zidler finally tells her that she was dying. just when she was on the very brink of actually getting away from the rouge and planning to go forth to run away with christian, and it's filled with grief and agony, satine knowing that she was sick and that sooner or later her illness was going to take its last toll on her, and to make things worse is when zidler makes her have to go convince christian that she didn't love him (to prevent him from being killed by the duke) the very last shot we see of the reprise 'today's the day when dreaming ends' shows us satine looking at the bird in a cage, just like what she did previously but this time, knowing that the dream to 'fly, fly away!' one that was so close to happening, had been abrupt.