Wiktionary defines it as:
A jocular coinage, apparently by students at Eton, combining a number of roughly synonymous Latin stems. Latin flocci, from floccus, a wisp or piece of wool + nauci, from naucum, a trifle + nihili, from the Latin pronoun, nihil (“nothing”) + pili, from pilus, a hair, something insignificant (all therefore having the sense of "pettiness" or "nothing") + -fication. "Flocci non facio" was a Latin expression of indifference, literally "I do not make a straw of...".
As for the reason for it being introduced in your spellchecker... well... Easter egg?
EDIT: actually floccinaucinihilipilification is listed in the OED, with examples dating back to the 18th century. So, well, it's a rare English word and was probably dumped in the spellchecker dictionary from a big list of words, used or not.