The first day of something—e.g., an opening day for a show or the first day at a job or trip. Can also be used adverbially as "from the first day."
その映画は来週の土曜日に初日を迎える。
That movie opens next Saturday.
新しい職場の初日は緊張した。
I was nervous on my first day at the new job.
初日から売切れが出るほど人気だった。
It was so popular that tickets sold out from the opening day.