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means The fourth note of the diatonic solfège scale, sung as a fixed syllable between 'mi' and 'sol' when learning or sight-reading music.

from From the solfège system devised in medieval Italy, where syllables were pulled from a Latin hymn to John the Baptist ('Ut queant laxis') whose successive lines happened to start on rising notes of the scale. 'Fa' comes from 'Famuli', a word in that hymn's text — chosen not for meaning but simply because it sat on the right pitch. So the note's name is really a scrap of liturgical Latin, conscripted into music theory and stripped of its original sense.