What is Edna's big resolve?
While I would echo what is said above, I would make it a little stronger and a little harsher toward what Edna rebels against, and add the sexual aspect of her resolve.
Much of what Edna experiences and attempts to do is motivated by an awakening of her awareness of the flesh. The sexual aspects are central to this, of course, but even her learning to swim is partly sensual, the feeling of the water on her skin, that kind of thing. Long dormant desires awaken and are part of her resolve to accomplish self-determination. This awareness leads to her withholding sex from her husband, which further demonstrates the connection between sex and her awakening.
And one shouldn't look lightly at the forces that lead Edna to rebel: society, the public, her husband, the double standard for men and women when it comes to sexual relations. Edna's resolve is to overcome all of these and determine her own present and future.
Unfortunately, she fails, and rather than go back to her old way of life she chooses to commit suicide in a final, fatal act of self-determination.
Throughout The Awakening, Edna's resolve is to live life on her own terms and to become a self-actualized person.
Her relationships with Alcee and Robert are opportunities to free herself from the repression she feels at the hands of both her husband and society as a whole. The two extended metaphors we see throughout the novella emphasizing this idea are the many references to the caged bird and Edna's own encounters with the sea. Through these images we come to realize her desire to live free from the expectations and limitations of society. Edna wants to explore and experience life on her own terms and on her own accord.