At the beginning of the story, Jerry thinks of the beach where he played as a child, the beach where his mother still goes, as the "safe beach." Later, he even thinks of it as a "place for small children," feeling insistent that it "was not his beach." In the beginning of the story, he thinks of the other beach as the "wild bay"; it has an element of danger, in part, because when he goes there, he is alone. His mother is back at the "safe beach," looking like a "speck of yellow under an umbrella that looked like a slice of orange peel."
In the "wild bay," however, Jerry is surrounded by "rough, sharp rock", and he can see other rocks that lie like "discolored monsters" beneath the surface of the water, down on the ocean's floor. Even the water has "irregular cold currents" that shock his skin. The "safe beach," then, seems to symbolize the security of childhood: our parents look out for us to make sure we are safe and cared for, to make sure we don't do anything too dangerous. On the "safe beach," Jerry is still like a little boy, hanging out with his Mum. At the "wild bay," Jerry is alone, and there is danger. He must navigate it by himself, just as adults must navigate the world without the security of their parents' constant presence.
Jerry doesn't want to abandon his mother, as he feels somewhat responsible for her happiness, but he also longs for greater independence from her, as he is eleven and reaching adolescence soon. The two beaches symbolize childhood and maturity, and Jerry's movement between the two is symbolic of his liminal position between being a child and being an adult.