Umm, well, "Alice's Adventures in Wonderland" doesn't really have a set plot; instead, it's rather a jumbled up collection of stories pieced together in a nonsensical fairy tale. (A plot has a set beginning, middle, end, and characters develop and have goals, ect). In fact, Lewis Carroll orginally told seperate stories to his two nieces that featured a girl named Alice in a fantasy world; eventually he combined their favorites into a novel; hence the lack of supporting, chronological acts (if you read each chapter on its own, regardless of order, it's bound to sound like a story of its own).
That being said, the Caterpillar plays the role of a rather stubborn guide. Her meeting him hardly alters the overall "plot" and he has little influence on her character.
When Alice first meets the Caterpillar he asks her to tell him everything that has happened to her. She tries to recount her adventures but is unsuccessful and becomes rather upset. Far from trying to comfort her, he simply repeats his questions until she gets so annoyed that she stomps away. He then calls her back and asks her what is wrong. Alice then seeks his aid by asking him how she can go back to her original height, and he tells her to eat the mushroom that he was sitting on. He then leaves (in the novel he doesn't turn into a butterfly like in the Disney movie, nor does he shout right before he leaves).
So really, the only thing he does is return her back to her original size, and not much else...
Hope this helps! :)