It's been a long time since I've read it, but if i'm not mistaken its about a woman who finds out her husband is dead and she's (GASP) happy about it.
I believe it's called the Awakening because by receiving the news, she feels like she is waking up from her old life and a new one is just beginning. One without her husband in which she can do whatever she damn well please. It's the start of her new life, and awaking means the start of a new day.
