Iris has the most beautiful lyrics of all the songs ive ever listened to. Infact this City of Angel soundtrack is one of my favourite songs ever.

"when everything feels like the movies, yeah you bleed just to know youre alive",
theyre relating the movies to the "perfect life"; where the sun is always shining and everything has a happy ending. But "you bleed just to know youre alive" refers to trying to break free of that perfect life and feel alive.

"And I don't want the world to see me... Cause I don't think that they'd understand.
...When everything's made to be broken.. I just want you to know who I am."
 
For me the chorus simply refers that in this reality when people underestimate every decision that we make, it is still the right place to live in since there are or there is someone out there who believes in you. And sad the lyrics may sound to the song, just knowing he/she exist is all that matters..