Alice stands before a large Caterpillar on a large mushroom and the Caterpillar is smoking a hookah. To be frank, a hookah is a very large water bong designed by the Persians for the purpose of smoking any number of drugs. In Victorian England, the hookah was a symbol for Eastern Wisdom and was associated heavily with non-Christian religious wisdom. The Caterpillar, then, is meant to be a kind of Wise Man or Shaman. (Remember Cocaine and other like drugs were still basically legal during this period, and the mind expanding qualities of drugs were honored in many circles. Freud was addicted to Cocaine, and Arthur Conan Doyle gave Sherlock Holmes a similar affliction).
The Caterpillar opens the conversation in a wise, but seemingly rude, way: Who are you? he asks.
Alice can't seem to respond very well, except to say that she is confused. The Caterpillar won't accept this, but Alice points out that he might understand better after he has transformed into a butterfly and sees what radical change is like. The Caterpillar does not agree with this idea though, and asks Alice to try and remember the school rhymes that she complains she has forgotten as part of her massive bodily changes.
Alice recites for him a poem called You Are Old, Father William.
Alice recites the poem, but it is changed from the original. In her new version Old Father Williams is old, but because of a good attitude and the leading of a healthy life he is able to perform all sorts of youthful feats, much to the dismay of his son.
Alice and the Caterpillar agree that the poem is not how it used to be.
The Caterpillar asks Alice what she wants and she replies that it's not any particular size that matters, its all the changing that bothers her. The Caterpillar disagrees and then leaves, but he does say that one side of the mushroom will make Alice grow bigger, the other smaller, seemingly leaving Alice with a tool to control her growth. Alice wishes she didn't have to argue so much with animals, and then goes on to experiment with the magic mushroom.
First she is too small. Then she nibbles the mushroom and her neck grows high above the trees where a pigeon mistakes her for a serpent. Finally Alice gets to be the right size and she sets forth to find that garden she saw in the first chapter. But then she comes upon a very small house and she decides to shrink herself to the appropriate size so as not to frighten the house's inhabitants.
In this chapter Alice is faced with the fact that change is natural and good, and that learning how to be both big and small, both an adult and a child, might be a good skill. After all, to be childish in old age seemed very healthy for Father William. One might speculate on the place drugs play in helping people to be both childlike and an adult at the same time. But as this a family web site, I leave that vein of exploration to the reader. The important thing is that Alice is beginning to learn that her changing person is the only constant thing, and that the appropriate thing to do is to figure out when certain aspects of her personality are appropriate. For example, when you come upon a four-foot high house, it is appropriate to shrink to that scale. That is, there are times for being small and times for being big. Adulthood is just about being big, it's about knowing when it is okay to be small again too.