the.com/quarterfinal

means One of the four matches that narrows a field down to the final four competitors.

from A straightforward compound of 'quarter' and 'final' — built in the 19th century as knockout tournaments (especially in British sport) needed a word for the round that whittles a bracket down to a quarter of its semifinal-bound size. No myth here, just tidy sports-administration logic: someone needed to label the round before the semifinal, and 'quarterfinal' did the job perfectly.