Prefix used with time nouns such as 日, 週, 月, 年 to mean 'the following day/week/month/year'. Not used as a standalone word.
The next day, he woke up early.
There is a meeting on Monday of the following week.
翌 is the common, everyday prefix for 'next' (翌日, 翌月), while 明 as a 'next/coming' prefix is rarer, more formal, and used mainly with specific dates.
次 attaches broadly to nouns to mean 'next' in a series (次回, 次世代), while 翌 specifically prefixes time words to mean 'the following' (翌日, 翌年).
The kanji 翌 is composed of 羽 (wings) and 立 (stand), but the historical derivation is uncertain. It is conventionally used to mean 'the following' in time expressions.
following accounting period; next term
next fiscal year; next academic year; next calendar year