The action or habit of judging something to be worthless.
Back in the eighteenth century, Eton College had a grammar book which listed a set of words from Latin which all meant “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 absolutely valueless (a verb, floccinaucinihilipilificate, to judge a thing to be valueless, could 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.
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 pneumonoultramicroscopicsilicovolcanoconiosis edged it out in the second). It had a rare public airing in 1999 when Senator Jesse Helms used it in commenting on the demise of the Comprehensive Test Ban Treaty: “I note your distress at my floccinaucinihilipilification of the CTBT”. (worldwidewords.org)