As Papyrus gave Frisk a piggyback ride around town, he admitted that he wasn't quite sure what to do at first so he asked Lora for help. The dragon had explained that Frisk was far too young to go on a real date and suggested a play date instead.
Frisk asked if Papyrus knew what a play date was, because they didn't. The cheerful skeleton replied that he had asked Lora the exact same question and proceeded to do an unintentionally funny impression of the luck dragon as he recited her explanation.
"A play date is when young individuals are brought together for the purpose of social interaction and fun."
Papyrus then asked Frisk what they wanted to do 'for fun'. The human had a few ideas, they still wanted to go to the library and they had spotted some kind of restaurant during their prior exploration of Stonedin but they also wanted to learn more about Papyrus. They weren't sure what to pick and worried they would choose something their friend didn't like, they asked Papyrus what he wanted to do.
He replied that he would take part in whatever activity Frisk wanted to do. Frisk just blinked at him and decided to not look a gift skeleton in the mouth. They decided to make it a play date of fun by reading at the library, then they both grab a meal at the restaurant and Frisk would spend the night having a sleepover with Papyrus.
* The idea of having so much fun with The Great Papyrus fills you with DETERMINATION.