"a v-shaped nick or indentation," 1570s, probably a misdivision of an otch (see N for other examples), from French oche "notch," from Old French ochier "to notch," a word of unknown origin. Said to be unconnected to nock. U.S. meaning "narrow defile or passage between mountains" is from 1718, mostly a New England and New York word for what is called further south a gap.
1590s, "cut a notch or notches in," from notch (n.). Earlier verb (before misdivision) was Middle English ochen "to cut, slash" (c. 1400). Meaning "to place in a notch, to fit (an arrow) to the string by the notch" is from 1630s. Meaning "to mark or score" (1837) is sporting slang, originally in cricket, from the old method of keeping score; notch (n.) as "a nick in a stick, etc., as a means of keeping score" is from 1570s (also compare score, tally). Related: Notched; notching.