The story
From nought (“zero”) + -ies (“plural of -y”), in imitation of the names of other decades (twenties, thirties, etc).
Etymology from Wiktionary, CC BY-SA 4.0.
noughties
Today it means: The decade consisting of the last year of the previous century and the first nine years of the next: from 1900 to 1909, 2000 to 2009, etc. Full definition →