Peter Pan himself (Symbol)
The titular character in the story, Peter Pan, is himself a symbol for eternal youth. He is the embodiment of the desire to never grow old and take on adult responsibilities. He transcends the inevitability of time by living in a dream world in which he is the leader of his own kingdom. The defining characteristic of Peter—the fact that he does not want to grow up, and that his top priority is staying without responsibility—is what makes him a symbol. Throughout the story, and in our culture in general, "Peter Pan" represents eternal youth.
Hook (Symbol)
Peter is not the only character who is a kind of symbol or representation of a concept or idea. His main adversary in Never Land, Captain Hook, is also a symbol, representing the oppressive paternal forces in society. If Peter represents eternal youth, fun, and adventure, Hook represents the opposite: the adult world, the squashing of fun, and a morose attitude that only a bitter adult could have.
Flying (Symbol)
One of the miraculous things that Peter teaches the Darling children is the ability to fly. His instructions are simple: if they think happy thoughts, they will become weightless and can fly anywhere. The flying in the story represents a kind of carefree attitude that comes along with youthful adventure, an ability to tap into one's happy thoughts to such an extent that they can lift one off the ground. Flying represents not only physical buoyancy and weightlessness, but also emotional and mental weightlessness.
Do You Believe in Fairies? (Symbol)
When Tinker Bell drinks the poison for Peter, she begins to die, but Peter incites whoever believes in fairies to clap their hands and pronounce their belief confidently. It is this speech act, this saying-out-loud of the audience's belief in fairies, that revives Tinker Bell. Thus, the act of stating one's belief in magic becomes symbolic of the survival of magic. It is belief that makes the impossible possible.
Ticking Clock (Motif)
The crocodile that is on the hunt for Captain Hook has swallowed a clock, so whenever Hook hears the ticking of the clock, he knows that the crocodile (who is intent on eating him) is nearby. The ticking of the clock becomes a motif in the story, representing the passage of time, and the ways that Hook is being pursued by the inevitability of death.