Riggan's ex-wife is one of the only normal people in the wacky world of Birdman. She's a center of stability…which, of course, Riggan pretty much ignores.
Maybe he ignores her because she's not particularly flashy or showy. She mainly just stands quietly by the sidelines, watching everything unfold and whispering in Riggan's ear like an angel on one shoulder (which definitely makes Birdman the devil on the other).
And what does Sylvia metaphorically whisper? That family's important.
Riggan's blinded by the play and his ego, so it's up to Sylvia to tell him to be there for their daughter and even console him about not being Farrah Fawcett (again, we thought that was obvious, but maybe if you do enough acting your own identity gets a little screwy).
And if you thought having the strength and the love to support a self-obsessed actor like Riggan is amazing, remember that Riggan cheated, or almost cheated, on his wife a) in their own bed b) at their anniversary party. Does it get much worse than that?
Actually, it does. When Riggan asks Sylvia why they broke up, she calmly responds:
SYLVIA: You threw a kitchen knife at me, and an hour later you were
telling me how much you loved me.
Wow. Knowing that backstory really amplifies Sylvia's saintly patience.