This is the 2435th most frequent Korean word.
날이
"날이" means "day" or "the day" in English.
Here '날이' refers to the current state of the weather.
날이 맑아서 밖에 나가고 싶어요.
The weather is clear, so I want to go outside.
In this sentence, '날이' refers to the flow of days or time.
날이 가면 갈수록 더 잘하게 된다.
As days go by, one becomes better.
This usage of '날이' signifies a specific, particular day.