A debutante is a young woman from a rich, high-class family who is shown to that high-class world for the first time. The old custom is a special dance, a debutante ball, where she 'comes out' — not out of a door, but into society, so important people can meet her. You will find this more in old novels, history, and society news than in ordinary talk. Some families in Britain and the American South still hold these balls; many other people now find the custom old-fashioned, even a little silly. Though actually, writers still use the word, and they sometimes stretch it to mean any young, polished, well-connected woman, even when there was no ball at all. It feels formal and a bit from another time.