1. What does it mean?
낼 contracts 내일. In plans and messages, 낼 보자 simply means 'see you tomorrow,' with a relaxed written feel.
Also written or said as nael
2. The nuance
It is not a different day or a special scheduling term. The same written syllable can also be a form of 내다 in another sentence, so read the surrounding grammar.
3. Examples
“낼 아침에 도서관 앞에서 만나자.”
Let's meet outside the library tomorrow morning.
“이 얘기는 피곤하니까 낼 이어서 하자.”
I'm tired, so let's continue this conversation tomorrow.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.