the.com/turn of the century

means The period marking the end of one century and the start of the next, usually used loosely to mean 'around the year ending in 00.'

from A straightforward phrase built from 'turn' in its sense of a pivot point — like the turn of a tide or turn of a page — fused with 'century' once that word settled into English (borrowed from Latin 'centuria,' a group of a hundred). The phrase itself is a simple, functional 19th/20th-century coinage, not a deep etymological puzzle — the real drama was never in the words but in the calendar math: does the new century start on the year 00 or the year 01? That argument is older and far more stubborn than the phrase describing it.