also: さいにち
noun
fast day; day of abstinence
A day on which one abstains from certain foods or activities, often for religious purification. Used in Buddhist and Shinto contexts.
今日は斎日だから、肉を食べない。
Today is a fast day, so I won't eat meat.
斎日には寺で精進料理をいただく。
On fast days, we have vegetarian cuisine at the temple.
精進日 also means a day of religious abstinence, but is more specifically associated with Buddhist vegetarian practice. 斎日 is a broader term that can include Shinto purification.
From 斎 (purification, abstinence) + 日 (day). The exact historical derivation is uncertain, but the word has been used in Japanese religious contexts for centuries.