Does the beach hold any significance in the story "A Memory?"
As the narrator ponders and revels in her recurring memory of touching her first love's hand on the stairs, she tries to frame her current view of reality (on the beach) literally and figuratively. She would literally hold her hands up, like a painter or photographer, and frame the scene:
From my position I was looking at a rectangle brightly lit, actually glaring at me, with sun, sand, water, a little pavilion, a few solitary people in fixed attitudes, and around it all a border of dark rounded oak trees like the engraved thunderclouds surrounding illustrations in the Bible. Ever since I had begun taking painting lessons, I had made small frames with my fingers, to look out at everything.
The narrator is trying to create a perfect observation, framed and still, the people in fixed attitudes (as if in a painting), all in a perfect landscape. She wants this image to be as perfect as her memory of her interaction with her first love. Therefore, she wants it to be picturesque, a perfect landscape. For her, the landscape must be still, like a painting, to be perfect. The beach and the landscape around it provide the narrator with a canvas upon which to frame this idyllic image, something she can add to the memory of her love, "where I would watch him with this hour on the beach accompanying my recovered dream and added to my love."
The narrator is self-absorbed and judgmental of the bathers. However, she (a teenager) is also beginning to discover herself, physically and mentally, so her self-absorption is a necessary phase in the course of self-discovery. When her love gets a nosebleed, she recalls this with horror and begins to worry about him as much as she pines for that moment on the stairs. Like the nosebleed, the intrusion of the bathers is a reminder that life is not a perfect, picturesque setting framed in stillness. This is a moment when she is trying to reconcile the idealistic memories and fantasies with the real world (represented by the nosebleed and the bathers, both of which intrude on this perfect memory.)
The beach is simply part of that perfect setting. But here is one interpretation that dissects the beach into two parts which symbolize fantasy and reality. A beach is the border where water meets land. The narrator identifies the sand with disgust because the bathers are playing with it. The water was still like the narrator's ideal, framed painting: "The water shone like steel, motionless . . . " The sand is reality and the water represents the still fantasy. The sand and water meet at the beach and this is a moment when reality and fantasy meet for the narrator.