Often done in early stages a relationship, a date where it's implied that the intent is to merely cuddle with no expectation of sex though it may lead to that if the chemistry is there. It's a step up from asking to simply hang out.
When a girl asks for a cuddle date, she may just want exactly that, to test the waters or to simply not appear to be a slut.
When a guy asks for a cuddle date, he's looking to get laid but either trying to be a gentleman by giving her an out if it doesn't go well or simply too shy to explicitly ask "hey, you dtf?"
Dude she asked me for a cuddle date, what's that?
Be chill, play your cards right and you might get some.