Back in the eighteenth century, Eton College had a grammar book which listed a set of words from Latin which all meant something of little or no value. In order, those were flocci, nauci, nihili, and pili (which sound like four of the seven dwarves, Roman version, but I digress).
As a learned joke, somebody put all four of these together and then stuck –fication on the end to make a noun for the act of deciding that something is totally and utterly valueless (a verb, floccinaucinihilipilificate, to judge a thing to be valueless, ccan also be constructed, but hardly anybody ever does). The first recorded use is by William Shenstone in a letter in 1741: “I loved him for nothing so much as his flocci-nauci-nihili-pili-fication of money”.
A quick Latin lesson: flocci is derived from floccus, literally a tuft of wool and the source of English words like flocculate, but figuratively in Latin something trivial; pili is likewise the plural of pilus, a hair, which we have inherited in words like depilatory, but which in Latin could mean a whit, jot, trifle or generally a thing that is insignificant; nihili is from nihil, nothing, as in words like nihilism and annihilate; nauci just means worthless.
Floccipaucinihilipilification (with a p in seventh place) also exists. Examples of that form are found online and in some modern books but it isn’t standard. The fault seems to be that of Sir Walter Scott, who misspelled it in his journal in 1829, a mistake perpetuated by the Guinness Book of World Records, which has included it in some editions as the correct form, quoting Scott, while noting the n version only as a variant rather than the original.
The word’s main function is to be trotted out as an example of a long word (it was the longest in the first edition of the Oxford English Dictionary but was edged out in the second by pneumonoultramicroscopicsilicovolcanoconiosis). It had a rare public airing in 1999 when US Senator Jesse Helms brought it out to comment on the demise of the Comprehensive Test Ban Treaty: “I note your distress at my floccinaucinihilipilification of the CTBT”.