Peter Pan's Shadow

One of the most memorable scenes from Peter Pan is his first meeting with Wendy, where he loses his shadow and she sews it back on for him.

In the book, the shadow is pulled off when Nana catches it and the closing window severs it. It's treated like a physical object; it's "quite an ordinary shadow" and Mrs. Darling rolls it and puts it in a drawer. This fits with the book's whimsical tone, particularly the scene where she first attempts to hang it outside, only to see that it "looked so like the washing and lowered the whole tone of the house." 

In the Disney adaptation and the later 2003 adaptation, Peter's shadow is alive. It is a mischievous, active creature that Peter has to chase and catch. This is clearly a choice to make the scene more exciting for the medium of film. Upon being reattached, it goes back to normal and is never mentioned again.
In the show Once Upon a Time, the Shadow is an demonic being that serves Peter Pan. In Peter and the Shadow Thieves, a children's sci-fi novel by Dave Barry and Ridley Pearson, where a being called Lord Ombra enslaves people by stealing their shadows. However, these more recent adaptations - which seem to draw more on the film versions with the living shadow - may miss the point behind Barrie's reasoning.

Peter's shadow is what first draws him to Wendy. 
His origin story is that he left his home while the window was open. He returned  returned to find that the window was shut and his mother had forgotten him. His encounter with Wendy, a new mother figure, repeats these elements in reverse. On his first visit, the closing window  traps his shadow. When he returns to retrieve it, he is able to enter the house and spend time with Wendy. They are parted when he forgets her, and at this point she becomes a mother in the biological sense.

There are plenty of literary references to the shadow becoming separated from the body. In The Wonderful Story of Peter Schlemihl, published in 1814 to general popularity, a man sells his shadow to the devil only to find that he is now shunned by society.
In Hans Christian Andersen's "The Shadow," when a man's shadow is detached, it takes on a life of its own and eventually usurps his identity.
​In Oscar Wilde's "The Fisherman and His Soul," which reads like a response to both "The Shadow" and "The Little Mermaid," the shadow is the body of the soul.
​In Jewish lore, demons are believed to have no shadows.
The shadow is an extension of oneself, symbolic of the soul, and without one, a person is lacking or not human.

The opening chapters of Peter Pan have the only mention of shadows in the book. However, in the "Fairy Notes" containing Barrie's ideas, shadows show up multiple times.

Note 210 reads, "Shadow of girl--P expected to find it cold--it's warm! Then she's not dead, &c." 206 mentions the idea that a warm shadow indicates that the owner is healthy, but the shadow's limp indicates that the owner has hurt her foot.
This lends itself to the idea that the shadow is the double of the body and can indicate whether the soul still resides there. Barrie also considered using shadows as psychopomps. In the final version, Peter Pan is briefly mentioned as a psychopomp: "when children died he went part of the way with them, so that they should not be frightened."

Note 95 says, "Girl suffering from want of her shadow - shadow also suffers, dwindles, &c," and Note 97, "Suppose you cd hurt Peter by hurting his shadow, &c, (as in Indian fairytale)." So Barrie took some inspiration from folklore and other literature. Note 99: "shadow is quivering {therefore} original is suffering somewhere."
James Frazer's The Golden Bough (1922) explains how the shadow is viewed as a kind of voodoo doll; the same in the "Indian fairytale" Barrie mentions. Someone could hurt Peter by hurting his shadow. This explains his urgency in regaining it.
[Edit 7/10/21: The "Indian fairytale" may be a legend referred to in The Golden Bough. In a section about superstitions that shadows are vulnerable, there is this :
“After Sankara had destroyed the Buddhists in India, it is said that he journeyed to Nepaul, where he had some difference of opinion with the Grand Lama. To prove his supernatural powers, he soared into the air. But as he mounted up the Grand Lama, perceiving his shadow swaying and wavering on the ground, struck his knife into it and down fell Sankara and broke his neck.”
Note that Sankara is flying like Peter Pan when he meets his demise. Another version, however, does not give the same implication that the knife causes Sankara to fall.]

On another note: Barrie's fairies are creatures of light. The nocturnal fairies in Peter Pan in Kensington Gardens are "bewilderingly bright." Upon her introduction in Peter Pan, we learn that Tinker Bell's light "was not really a light; it made this light by flashing about so quickly," but when she lies dying, "her light was growing fainter; and he knew that if it went out she would be no more." Onstage, she was portrayed by shining a light. So these otherworldly beings are creatures of light.
In folklore, fairies were connected to the souls of the dead and their realm to the underworld. In contrast to these glowing beings, the dark shadow identifies Peter as both a living being and someone with a soul.
Peter is a psychopomp himself, only on the verge of being human. He tells Hook that he is "a little bird that has broken out of the egg," hearkening back to Peter Pan in Kensington Gardens, where human babies are originally birds and Peter learns to fly from birds. But he still has a shadow, and this mark of humanity is the thing that leads him briefly away from the otherworldly realm of death and back to a family. In the end, he leaves that family, but continues a cycle of return where he takes Wendy's descendants one by one to Neverland.
​
Neverland is an indulgence of childhood, the manifestation of the children's imagination. Their games and daydreams shape it; Wendy's imaginary pet wolf lives there. Even when they live there, their food is make-believe.
Actually, this book presents kind of a horrible picture of children. They are innocent, but also heartless and don't care about anything. Arrogant, self-absorbed Peter is the most obvious example, but the Darling children abandon their parents without a second thought. It's Wendy's growing maturity that causes them to go home. 

SOURCES

• Anon: A Play. One of the first versions of the Peter Pan story.
• Corcuera, Alfonso Muñoz and Elisa T. Di Biase. Barrie, Hook, and Peter Pan: Studies in Contemporary Myth; Estudios sobre un mito contemporáneo. 2012.
• Friedman, Lester D. and Allison B. Kavey. Second Star to the Right: Peter Pan in the Popular Imagination.
• J. M. Barrie Discussion Board. "Original version of the play."
• Stirling, Kirsten. Peter Pan's Shadows in the Literary Imagination.
• Swank, Kris. The Shadow-Self and Coming of Age in George MacDonald’s Phantastes, Ursula Le Guin’s A Wizard of Earthsea, and J.M. Barrie’s Peter Pan.   2015. Contains some the notes on shadows from "Fairy Notes."