The NEXT plans allow you to upgrade after 12 or 18 months, depending on the plan you choose. If you choose to upgrade at 12/18, you give them back your old phone (provided it's still meets the condition standards) and they relieve you of the rest of the payments you owe. You can then start a new NEXT plan with a new phone.
Depending on the resale value of your phone, and how many payments past the 12/18 you made, it could be a good deal or bad deal. My gut tells me that early upgrades on NEXT for iPhones is a bad deal since you'd probably get more than AT&T is letting you off the hook for.
Math shown below.
Get new iPhone 6 ($650) using NEXT12. You pay $32.50 for 12 months and decide to upgrade. You've paid them $390 and have $260 remaining. You pick a new iPhone (or whatever) and start over. AT&T lets you off the hook for the $260, essentially paying you $260 for a 1 year old iPhone6. I think you could do better selling it yourself on eBay or Craigslist.
The NEXT18 plan is even worse since at $27.09 for 18 months, you've paid $488 and have $162 left. AT&T is paying you $162 for an 18 month old iPhone6. That's robbery.
If you want to upgrade early, you're better off buying at full price and selling it whenever you want to. Plus, it'll be an unlocked phone, so you might get a few more bucks.