It seems to me that "Through the Tunnel" is a story about an adolescent's struggle with his own identity (or, we could say, his quest to establish his own identity) and his desire to be wanted and accepted by others.
As the story opens, readers learn that Jerry, who is on vacation with his mother, is eleven years old--a time during which many boys begin to distance themselves from their parents. On this vacation, Jerry desires some time away from his mother, and ventures away from the family beach to the "wild bay." Once there, he encounters a group of older boys, who seem to be natives, and who don't speak English. Jerry watches them go underwater for an extended period of time and resurface beyond a large rock wall.
The rest of the story focuses on Jerry's attempts to swim through the tunnel, and while readers might think at first that he's doing it to impress the boys, the sense of accomplishment Jerry feels when he finally performs the task lets us know that Jerry wanted to swim through the tunnel for himself. At the end of the story, he has successfully strayed from his mother and has done something both dangerous and daring--and he has survived.
This sort of depends on what you think the less deep meaning is.
I think you can say what the first answer says. It is clearly a story about facing up to your fears and overcoming them. Jerry manages to do this very bravely.
But you can also say that this is a story about being an individual -- a story of a young person coming of age and becoming his own person. If you look at it this way, the bravery he shows in going through the tunnel is secondary. What the story is really about is how he learns to be his own person who does not need his mother and does not even really need the approval of the boys that he envies at the start of the story.