The meaning “month” developed from “moon” and is already attested in the earliest Old Turkic sources. Old Turkic calendrical usage counted days from the new moon; Erdal therefore notes that the months were moon-months, though they were not all purely lunar because they did not drift through the seasons.
The first vowel was long: Clauson writes a:y, Räsänen āj, and the inherited length is independently supported by modern Turkmen and Khalaj.