What does it mean for a boy to call a girl aunt?

If it is just a normal relationship between men and women, it has two meanings: one is a joke. The other is to laugh at each other, saying that they look like aunts, talk like aunts (nagging), and handle things like aunts.

If two people are lovers, a boy says this to a girl, which only shows that the boy is a nickname for the woman, not its meaning.