Juliet is on the balcony talking about Romeo and that a name doesn't make the person.  She continues to talk about how great her love is for Romeo and says that she is all Romeos and he hears her and chimes in that he wants to be with her.  She is then startled by the appearance of a stranger below her balcony.  The exact lines are in Act II, Scene 2, Lines 48-51.

It is less a specific thing than the fact that Romeo overhears her when she thinks she's alone. She is talking to herself about how intensely she loves him, and he over hears her; that is what she says would make her blush.