adverb
Describes a gradual change or progression that happens each day. Often used with verbs of change like 変わる, 増える, 成長する.
日に日に暖かくなってきた。
It's getting warmer day by day.
彼の日本語は日に日に上達
His Japanese is improving day by day.
adverb
Archaic use meaning 'every day' or 'daily'. In modern Japanese, 毎日 or 日々 is used instead.
古い文では「日に日に」が「毎日」の意味で使われることがある。
In old texts, 日に日に can be used to mean 'every day'.