Something to grow into?

There was this guy talking to friend who was giving a coat to child and saying this: here’s for you to grow into, it was mine.

do you understand such a phrase?

Well, the man’s coat is still a little too big for the child but soon it will perfectly fit so the child can grow into the man’s coat.[YSaerTTEW443543]

TOEFL listening lectures: The professor mentions watermelons as an example of what?[YSaerTTEW443543]