increasing daily; day by day
Used as an adverbial noun, often with に, to describe something that grows or intensifies with each passing day.
It's getting colder day by day.
foodstuffs left out for many days
Rare, archaic noun referring to food that has been left out and accumulated over days. Primarily encountered in the compound 日増し物.
See also: 日増し物
His Japanese is improving day by day.
The word 日増し物 was used to describe the state of food preservation in the past.
day by day; with each passing day
leftover food; food kept for many days
Compound of 日 (hi, 'day') and 増し (mashi, 'increase'), literally 'day increase'. The exact historical derivation is uncertain, but the meaning is transparent from its components.