To sleep on it is to wait until tomorrow before deciding. Let me sleep on it, better sleep on it, they slept on it.
The advice holds up: sleep consolidates memory and reorganises what you learned, and hard problems really do look different in the morning. It is also a polite way of not saying no immediately. Most languages have their own version of the phrase.
1phrasesleep on itTo wait until the next day before deciding.
“That's a big offer, so let me sleep on it and I'll call you tomorrow.”
sleep on it is a delaying.
Practised in Idioms, Thinking & Memory