counter
counter for nights
Used with numbers in the ichi, ni, san counting system (e.g., 一夜, 二夜). Not used with the hitotsu, futatsu system.
旅館に二夜泊まった。
I stayed two nights at the inn.
彼は三夜連続で徹夜した。
He stayed up all night for three nights in a row.
晩 is a counter for nights or evenings, often used in the hitotsu, futatsu system (一晩, 二晩), whereas 夜 uses the ichi, ni system.
The kanji 夜 means 'night' and is used here as a counter with the reading や, which is a standard Sino-Japanese reading.