When you know your life is just once and it doesn't last forever, and you feel the joy of life. And you're no longer thinking only about your own things but making someone happy makes you happy, you're an adult, even if you're 13. That's what adulting means in my eyes.
To me, I guess it means being mature and knowing your stuff as well as starting to take charge of your life and your decisions. But on the other hand it can also mean learning how to do things for yourself outside your parents, such as scheduling doctor's apointments or eye tests. Or doing your own washing etc.
Just because you're over 18 doesn't mean you're an adult to me. If you don't have a job, you're not going to school, not paying your way through life and living off your parents you're a child to me.
I guess financial independence, networking for the sake of work/school, being able to supportive yourself emotionally if nobody else is there, general chores, time management, social norms, knowing consequences of your actions before making a decision, etc