When Holden Caulfield walks toward the Museum of Natural History, he recalls his field trips there when he was younger and thinks about the permanence of everything inside.
After he purchases theater tickets for his date with Sally, Holden decides to go to the park in order to get away from Broadway, where many people are rushing to buy tickets to the movies. Holden is disgusted with their eagerness because he finds most actors to be "phonies." When he reaches the park, he asks a little girl if she knows his sister Phoebe, and the girl tells him that Phoebe is probably in the museum. As he walks away, Holden remembers that it is Sunday, so his sister will not be there. Nevertheless, he dons his red hunting hat and walks to the museum. Once inside, Holden thinks to himself,
It always smelled like it was raining outside, even if it wasn't, and you were in the only nice, dry, cozy place in the world. I loved that damn museum.
Holden loves the museum because there is a permanence to it:
...in that museum was that everything always stayed right where it was. Nobody’d move. ... Nobody’d be different. The only thing that would be different would be you.
In his angst, Holden cannot fail to recognize the impermanence of life, something that has been tragically proven by his brother Allie's death and the death of James Castle, who could only fight against the other boys by jumping to his death.
In the museum, the encased Eskimo prompts Holden to think that
...certain things...should stay the way they are. You ought to be able to stick them in one of those big cases and just leave them alone.
This is the idea that Holden ponders as he leaves the museum and walks around.
The museum represents childhood memories of school field trips for Holden, reminding him of a time in his life when things were simpler and when he was happier. Allie, his younger brother, was still alive then and all in all his family was much happier as well. More importantly, however, the museum is a place that never experiences change. This also is important to Holden because all the change he has experienced in his life has been negative: his brother Allie's death, the effects that death has had on his family and friends, the effects on his academic progress, his repeated expulsions from schools and his having to become accustomed to more new people, etc.
Not only does it represent childhood memories for Holden but the museum also represents how Holden doesn’t want to grow up. It struck out when he started mentioning the fact that the museum never changed, only the person who visited the museum changed. He talked about the fact that he wished time would freeze just as the figures in the glass cases were frozen in time, this shows just how scared Holden is of growing up, he isn’t talking about it age wise, but more along the lines of seeing the world in a different light. He hates how the world around him changed every year he visited.