What is an important line or quote and what is its important?
Oh, this play is so much fun that there are many lines that are important because they show Shakespeare's wit and the playfulness in love that can happen. That said, I'm going to go with one of the other undercurrents from the play: the seriousness when love goes wrong.
Lies have been told about Hero (and her virtue), so that she is accused of being disloyal at the very moment when she's supposed to be married. Eventually, via a complex plan, the man she was to marry must marry an unknown woman of another's choosing, who turns out to be…Hero. They get back together, a triumph of love, and all is happy…but the line below shows how badly she was hurt by the first lies, and how much she is revived by the return of love:
"And when I lived I was your wife: / And when you loved, you were my other husband."