Young lady is a mode of address to a woman in her twenties, but it has also become a very popular mode of address to a minor girl; a case of belittling language clad in words that sound like the opposite.
It comes with some irony when used for a child (often, a pre-teen) who is far from being a lady. Although by itself friendly and not impolite, the title has certain subliminal connotations along the lines of "you are still a little girl" or "we expect you to behave like a lady (but you are behaving like an ill-mannered little girl)".
A girl is often addressed "young lady" when she is reproved for misbehavior, e.g. by her mother, father, grandparent, governess, teacher, or any other authority. It is used in second person (e.g. "Young lady, come here at once!") and in third person (e.g. "Can you give me a hand, darling? This young lady needs to be taught a lesson.")
"Young lady" is a very popular phrase in spanking literature, spanking movies, and in spanking roleplay. Many female adult spankees love it when they are called "young lady" in a stern voice to start some roleplay/spanking activity because these two simple words can be enough to raise a whole wave of emotions.
The corresponding male counterpart is young man.