The forest creatures and title characters of this movie got their name when Mei, the little girl who first sees them in the film, mispronounces the word "troll". At one point in the original Japanese language version, when Satsuki first finds Mei sleeping in the grove behind their house, Mei tells her sister she saw a "totoro". Satsuki replies, "Totoro, do you mean troll, from the storybook?" and Mei nods in agreement. This aspect of the story was left out of the 1993 Fox English version, probably because the difference between ""to-ro-ru" (the Japanese pronunciation of "troll") and "to-to-ro" would have been lost on English-speaking audiences. The quote is included in the 2006 Disney English version.
The film is partially autobiographical. When Hayao Miyazaki and his brothers were children, his mother suffered from spinal tuberculosis for nine years, and spent much of her time hospitalized. It is implied, yet never revealed in the film, that Satsuki and Mei's mother also suffers from tuberculosis. He once said the film would have been too painful for him to make if the two protagonists were boys instead of girls.
Hayao Miyazaki originally conceived the characters Satsuki and Mei as a single girl. He wanted to add suspense to the latter half of the film, and he felt it wouldn't work with just a single girl, so he split her into two separate girls. The original girl had features of both Satsuki and Mei, and was 7: halfway between the ages of Satsuki (10) and Mei (4).
The trivia item below may give away important plot points.
Totoro actually comes from Mei mis-pronouncing Tororu which means troll in Japanese. This comes from a book Mei had read that turns out to be the Billy Goats Gruff as can be seen in the end sequence with mother with that book and if one looks closely it is seen to have a totoro on the cover.