The usual interpretation is that the "safe beach" represents the comfort and security of Jerry's childhood and his mother and the rocky, "wild beach" represents the unknown adolescent future without his mother. The "tunnel" is a challenge or rite of passage or test Jerry must pass to gain access to that future.
His determination to be able to swim through the tunnel like the older French boys stems from a desire to test himself, to discover new abilities, both in his body and his will. It is telling that much of the story has to do with the analytical way Jerry goes about preparing himself for the attempt to swim through the tunnel; unlike the French boys, who seem to Jerry to effortlessly go through, he has to approach things very carefully. He approaches it like a job: he practices holding his breath, he thinks about how long he will need to be underwater, he even requisitions from his mother the necessary equipment (the goggles).
Of course his mother has no idea of what he is up to, but probably, in real terms, neither does Jerry despite his analysis of the task itself. He doesn't want to impress the French boys or anyone else. There is no sense from the story that he is interested in exploring the tunnel, on the contrary, he dreads meeting with an octopus in the tunnel. The process of preparing is uncomfortable and causes him to have tremendous nosebleeds. He just feels an unexamined need to do it. So he does.
Once he does, the spell is broken. The resolution of the story is that Jerry does not object when his mother tells him that he should not go back to the beach that day: "It was no longer of the least importance to go to the bay."
I think if we are to understand the tunnel as a "rite of passage," the nature of this rite says a great deal about Jerry and his relationship to his widowed mother. Jerry's motivation is completely internal. We can understand it as his desire to get away from his mother, to assert his independence, but actually nothing has been asserted, other than his own will. And the result of his adventure is to return to his mother. He has been changed, but not in the way you might think. He wants his mother to be proud of him: he blurts out at the end that he can hold his breath for two minutes, but his mother pays little attention. "Don't overdo it," she says. Jerry cannot tell her about the tunnel. He has a secret he keeps from her now.