"manner;" late 14c., "melodies, strains of music" (a sense now obsolete; see musical senses below), from Old French mode and directly from Latin modus "measure, extent, quantity; proper measure, rhythm, song; a way, manner, fashion, style" (in Late Latin also "mood" in grammar and logic), from PIE root *med- "take appropriate measures."
Meaning "manner of acting or doing, was in which a thing is done" is by 1660s. Sense of "inflectional category in conjugation" is mid-15c. In music, 1670s as "method of dividing the intervals of the octave for melodic purposes" in reference to ancient Greek music; by 1721 in reference to modern music.
"current fashion, prevailing style," 1640s, from French mode "manner, fashion, style" (15c.), a specialized use of the French word that also yielded mode (n.1).