pre-noun adjectival
the ... after next; two ... later
Pre-noun adjectival used before time-related nouns (e.g., 日, 週, 月, 年) to mean 'the day/week/month/year after next' or 'two days/weeks/months/years later'. Common in formal and written contexts.
翌々日には結果が届く予定です。
The results are scheduled to arrive the day after next.
会議は翌々週に延期された。
The meeting was postponed to the week after next.
翌 means 'the next' (e.g., 翌日 = the next day), while 翌々 means 'the one after next' (two steps ahead).
明後日 specifically means 'the day after tomorrow', whereas 翌々日 is a more formal, written equivalent.
Reduplication of 翌 (よく, 'next') to express 'the one after next'. The reading よくよく is a regular reduplication reading.