In the original novel Neverland is a place where children go in their sleep, but the story also makes clear that Peter Pan and Neverland are very real and thus possible to reach while awake. And that Wendy & her brothers were the first children to really meet Peter and get to Neverland while awake. And after that Wendy's daughter Jane, and Jane's daughter and her daughter's daughter and..."so it will go on as long as children are gay, innocent and heartless." (And why it was just the daughters is because they were Peter's mothers in turn.)
The original novel also makes clear that Neverland is a seperate entity that can "think" and influence.
The director P.J. Hogan wanted to have the viewer ponder if in this movie version the story was really happening or not. Maybe it was just Wendy's fantasy during her last night in the nursery, before her father would force her to grow up and start the life of a young lady? Or perhaps it all really happened? It's totally up to interpretation. Although the fact that Wendy's telling stories about Hook and the other pirates but does not know anything about Peter Pan before his father makes the unpleasent decision, speaks for the fantasy point of view. As does the fact that in this movie Neverland doesn't seem to have links to dream world.
But there is at least one way to explain this through the really-happened point of view.
I personally prefer taking that point of view, because the movie is amazingly novel-faithful - and it irritates me to think that its base would've been taken so far from it in crucial matters by visioning it to be just Wendy's fantasy. Oh no, no way! So, here follows my own interpretation which keeps its base faithful to the original story wherein it all really happened:
What if, in the movie, Neverland is a place subcinsciously connected to every human's inner child, but not through dream world. That would explain why even adults started to unintentionally chant about how they believe in fairies, and did so while being awake.
And Neverland being connected to people's inner child, contacted the 12-years old Wendy who was dangerously close to teenage years but wasn't ready yet. So Neverland "called out" to Wendy by feeding her inner child with details about Hook and the other pirates which Wendy then brought out in her stories, not sure of where the characters come from. That, and the fact Wendy was in between childhood and teenage years is the reason why she was not surprised when meeting a flying boy with a runaway shadow - but on the other hand she did not believe in fairies. Neverland had touched Wendy with only some details about its pirates, but not their full stories. Because characters like Peter Pan and fairies had no place in her stories that are adventures of brave heroines such as her version of Cinderella.
In Neverland, when John spots the pirates from Wendy's stories - especially Hook - Wendy's reaction can be interpret in many ways; including that she started thinking of the amazing revealation that the characters in her stories come from a real place. The fact that Wendy did not know Neverland has maremades, speaks for that her likings do not affect Neverland's recidents but Neverland brings some of them to her inner child. Also, "Thus Wendy first laid her eyes on the dark figure who haunted her stories, she saw the piercing eyes...and was not afraid, but entranced." - could be interpret that she was looking at, not her own creation but someone she'd subconsciously "heard of" and found thrilling, and now got to see for real.
This point of view of course, does not explain how the pirates exist in a place that is not on this planet and not even enforced by imagination. Especially as Hook did not even know how to fly until he made the children tell him. But then again, this movie does borrow some elements from Disney and a line from the movie Hook in which vision Neverland is real and the pirates were able to travel between Neverland and Earth, though we're never told how. This movie's indication of them being able to leave is in the moment ("A moment of silence for our fallen enemy, Peter Pan. ...We sail at dawn!") - so if they were able to leave, there had to be a way for them to have arrived.
Perhaps there was another way, another gate, for this specific type of grown-ups to move between the planet Neverland an the planet Earth. After all they were not your typical grown-ups. Even the original script distinguishes children, pirates and grown-ups into three different groups of people. (By Hook's line "Grown-ups organize the world where children and pirates play in.") All this has convinced me that in this movie there was a way for the pirates to enter in and out of Neverland but it wasn not by flying. Maybe some day I'll figure out what it is.
In my opinion this Neverland-calling-out-to-Wendy vision suits the love story too. Wendy was meant to find Peter Pan and Neverland in order to learn how important it is to grow up and by falling in love with Peter she was capable of holding on to her inner child and the memories made, while growing up in this word that turns the best of us into too much an adult. And Peter was meant to find Wendy in order for her to have that experience and for his own pain to lessen, and for him to learn how "to live would be an awfully big adventure".
That the grown-up Wendy knew about events she had not been present at, may have but does not force, the story to be her fantasy. After all, Wendy never told us that Peter tried to close the window - we only see it happening. Wendy appeared to know only that Peter had visited her window and seen Mrs. Darling sitting at it. That much he could've told her on the way home, as she was worried about their parents having forgotten them. Wendy told about how Hook tried to poison Peter and what the poison was made of. Well, it is most likely that Hook himself revealed it on the ship while waiting for Peter to die of the poison.
Thus, it is completely possible this movie's story happened for real and exactly as the gorown-up Wendy rememebers it, but it can as well be interpret as only her fantasy. I support the really-happened view because that's how it is in the original novel and even as an indpeendent story it makes this much more tragic. I believe that the movie production too intented it so because originally they even filmed an adaptation of the last chapter from the novel, in which both Wendy and her daughter Jane met Peter Pan and thus it could not have been just Wendy's fantasy. They just chose to change the ending of the actual movie, for one, to allow the viewer some room for interpretation.