There are two options- (Assuming you are on AT&T, but it's more or less the same for Tmobile's JUMP or the Verizon one)
You can trade-in your current phone for a new one after 12/18 months w/o paying anything upfront but you'll always have a monthly phone loan payment until you pay it off.
You can payoff the phone anytime. So when you are ready to upgrade, pay it off and sell it and go for the one you want either through NEXT or outright purchase.
You are better off doing #2 IMO as you'll own the phone and can sell it for more than what you owe.
So your on the Next 18 which is a 24 month installment. After twelve months if you want to upgrade you would need to pay the additional 6 months and trade the device back in or pay off the rest of the balance and keep the device.