It's not like this scene was unexpected. But when it happened, it really defined how Emma views people and life in general. She doesn't trust easily, not only because her parents weren't with her, but because her guardian didn't protect her.
When Emma believed that Henry was dead
This scene was really heartbreaking. Henry was Emma's hope and when she didn't believe him, she realized that she had to do everything she could to make sure he was okay. Once Henry's life was on the line, Emma started believing, not only in the curse, but in herself to be there for Henry. To go through all that and have Henry die was too much for Emma, and she finally allows herself to express an emotion she's resisted for a long time. Love.