How Verizon phone plans work after they got rid of their 2 year plan?

I'm rough on my phone and because of that my parents don't want to buy me a new one, and I get it. I've been working for a year and I'm really proud of myself, i finally saved up enough to by a new phone. I want the iPhone 6 or 6s but I want to get the best deal. My parents won't talk to me about buying a new phone cause they don't think I'm serious about buying my own phone but I'm. I'm with Verizon and people say they can still trade in their phone even after the 2 year plans ended. I've had the iPhone 5c for about 2 and a half years. Can anyone explain to me how Verizon phone plans work?

Verizon and most other carriers do installment plans for phones now. Instead of locking you into a two-year contract, they lease the phone and you pay it off over time as part of your monthly bill. Usually the payments are split up so you'd pay it off by about two years.

You can pay it off earlier if you want, of course. If you decide to cancel your plan then you have to pay off whatever's left of the phone right then.