I know this has been beat to death the last few pages but I think this is probably the clearest explanation given for AT&T Next. Found on reddit.
Disclaimer: I don't work for AT&T, nor do I sell phones, nor do I care at the end of the day what plan you have. I'm just a guy who did a lot of homework and likes people having accurate information.
Summary
AT&T Next (and Verizon Edge) basically allow you to divorce the act of owning and paying for a phone, from paying for cellular service.
Background
All currently available mainstream plans feature two components- a DATA charge, and a LINE charge. We will ignore the DATA charge aspect from here on out, because it's the same regardless of what plan you choose.
AT&T Next offers you a lower monthly line charge ($15 less for data plans under 10gb, $25 less for 10gb
and over) in exchange for them not giving you a large subsidy when you buy your phone. Next plans never involve a contract, and you can get out of them at any time, penalty free, by paying off the balance you owe on your phone.
Apples to Apples Comparison: Keeping a phone for two years
Let's start with the simplest case, and assume you are going to buy a phone and keep it for two years. Whether you save more on a contract or Next here depends on whether or not your data plan is 10gb or higher, as AT&T bumps the line charge from $25/mo down to $15/mo at that threshold.
All examples assume a new base iPhone 6. Cost of acquiring and line charges after two years:
Next plan, = 10gb: ~$40 sales tax on new phone + ($15 x 24 line charge) + ($27 x 24 phone payment) = $1048
As we see here, you pay slightly more for a Next plan versus a contract if your data plan is under 10gb. However, that $88 buys you the flexibility to exit the deal at any time you want. If you are 10gb or over, you get the best of both worlds, saving about $150 over two years being on Next, plus you retain full freedom to walk away at any time.
So how does Next make AT&T money?
On trade-ins. Next gives you the OPTION, but not the obligation, to trade in the phone after either 12 or 18 months, depending on which payment schedule you choose. Should you choose to do so, you send the phone back to AT&T (it must be in salable condition), and in exchange, they forgive the remaining balance that you owe.
Example: Month 18 of "Next 18" plan: Amount owed on phone is $27 x 6 remaining months = $162. However, an 18 month old iPhone is worth substantially more than $162. A better option is to pay off the $162 so that you own the phone free and clear, and then sell it on your own for something around $350. Then just rinse and repeat with a new phone; as AT&T isn't paying for any of the phone, there's no cool-down period to start over as there is when on contract.
Summary
On a new iPhone, a Next plan may be slightly more expensive over two years with a small data plan, or a good deal cheaper with a family sized data plan. Either way, the ability to walk away at any time without penalty by just paying what you owe for the phone is a valuable thing. Trading in the phone leaves money on the table, but if you keep the phone the full two years, or pay it off and sell yourself earlier, there are few downsides to going with the Next plan.