counter
nth; number ... in order; ...-th in a sequence
Ordinal counter used after a number to show position in a sequence: 一番目, 二番目, 三番目, etc. It is more explicit about order than plain 番.
See also: 目
彼は三番目に到着した。
He arrived third.
二番目の角を右に曲がってください。
Please turn right at the second corner.
noun
division of a kabuki performance
Kabuki-specific noun for divisions or sections of a performance; this is a technical use and is not the ordinary everyday meaning.
歌舞伎で「番目」は上演の区分を指す用語として使われる。
In kabuki, 番目 is used as a term for a division of a performance.
Formed from 番, meaning number, turn, or order, plus 目, a common ordinal suffix. This is a practical component explanation rather than a detailed historical derivation.