day something happens; day one encounters something
Refers to a day when a particular event occurs or when one happens to come across something. Often used in contexts like lucky days or days of occurrence.
Today is the lottery drawing day.
It was truly a lucky day to run into him.
Compound of 当たり (atari, 'hit' or 'encounter') and 日 (hi, 'day'), with rendaku voicing to び.