The most important thing that Robert did for Edna was teach her how to swim. While this might not seem like a big deal, the idea of swimming becomes symbolic as the novel progresses. As Edna's abiltity and confidence in her swimming grow, so does her understanding of herself and how she feels about her position in society as a wife to Leonce and a mother to her two sons.
In the beginning of the novel she can hardy swim and needs to be holding on to someone else for security -- just as she holds on to Leonce and the traditional role of women in this society. As she learns to swim independently she becomes more independent in her attitudes and behavior. Robert takes her away from the house and spends a lot of time with her. She realizes there is more to what she wants from life than just hearth and home. By the end of the summer she is a confident swimmer and seems to have made a decision to be with Robert, but he upends her vision when he announces he is leaving for Mexico to make his fortune. Interestingly, that doesn't stop Edna's awakening.
Once she returns to town she stops her social engagements and eventually moves into her own house around the corner from her old house with Leonce. She even has an affair with Alcee Arobin. She is more truly her own person, and when she realizes that the dream of Robert will never come true she returns to the sea again. This time she swims until she is so far out that she can't return. She is not afraid to be alone out there -- she chooses to be alone and she chooses to swim away from a society she will never be happy or be herself in. She lets herself drown and be free rather than tied down.