When you are completely dependant on yourself for all your needs and wants. For example:
doing your own laundry
cooking your own meals and cleaning your own dishes
paying for your own car, car insurance, health insurance, cell phone, college education, clothes and toiletries
paying rent, even if you live in your parent's home, if you declare your independance from them, you owe them rent, utilities and groceries
To the child of Kelly G:
Honey,
Being an adult is boring. It's hard work and no one cooks for you when you don't feel like it and no one brings you soup when you're sick. I'd rethink declaring my independance until AFTER you get them to pay for college, by the time you graduate from college you'll be able to get a great job and afford all those freedoms and no one would expect you to move back home. Anyway, college was fun!