a noun is a word that is used to refer to a person, place, thing, idea, emotion, or phenomenon. 'Day' can be used as a noun to describe a 24-hour period or a certain day (e.g. to describe someone's Monday). The rules for using 'day' in a noun form are fairly straightforward; nouns are almost always preceded by an article such as 'the' or 'a' or other similar words.
1. The day was bright and sunny.
2. Monday is the beginning of the work day.
3. I'm always up for a day at the beach.
It's important to note that when using 'day' as a noun, it often needs to be pluralized to indicate multiple days (e.g. 'I'm taking three days off this week' instead of 'I'm taking three day off this week').