the other day; recently; some days ago
Formal or written expression for a recent past day. Often used in letters, announcements, or news reports.
過日お送りした書類はご覧いただけましたか。
Have you had a chance to look at the documents I sent the other day?
a day in the past
Rare, literal use referring to any past day, not necessarily recent. Mostly found in fixed expressions or older texts.
過日の出来事を振り返る。
Look back on events of days past.
過日、記者会見が行われた。
A press conference was held recently.
過日 is an equally formal, literary word for 'the other day' often seen in letters, essentially interchangeable with 先般 in tone.
Compound of 過 (past, exceed) and 日 (day). The reading かじつ is the on'yomi for both characters.