What does it mean to find your own?
To find your own has a lot of things to refer, it can refer to become responsible of your own self like finding a living by your own and not being dependent to anyone. It talks of being independent in every way.
It means to find your own place in the world! What you want to do with your life! A person coming into their own is growing up! That's the best way I can explain it! Good question!