Until very recently, the only way to purchase a decent refurbished used cell phone was to purchase it directly from a reseller; mobile phone carriers had not yet identified the gap in the market.  After realizing that existing customers were upgrading and switching to newer handsets, the carriers saw the potential that offering refurbished cell phones had for their businesses.  Most of the mobile carriers now offer to their customers a good variety of used cell phones that have come from several sources.

Phones that are Returned:  Most mobile service providers offer a 30 day trial period on new phones and allow returns, no questions asked, for that period.  When users try a phone and realize that it isn't for them (buyers remorse) or decide to go with a different phone, the provider has to find something to do with the phone they return.  Since most of these phones are barely used, the provider can refurbish the phone fairly easily by cleaning it up, clearing the memory, and re-installing the most recent software available.  They are then able to offer the phone to customers at a discounted price, even though it is essentially brand new.

Updates:  When customers upgrade their current phone to a newer model, they are often given the opportunity to "recycle" their old phone via the carrier.  Phones are "recycled" by manufacturers in that they are returned to the manufacturer that fixes any physical problems, reinstalls the most updated compatible software, and generally cleans them up.  Once refurbished, the phones are sold back to carriers and third parties who offer them as used cell phones.

Direct From the Manufacturer:  Mobile phones that have been returned to the manufacturers, for a variety of reasons, are very often refurbished and resold to the mobile carriers; these phones are in perfect working order, and often offered at little to no cost to customers signing up for a new contract with their carrier.

Why Buy from a Carrier?
Of course, the main motivation for buying used or refurbished cell phones is to save money.  Beyond the cost savings, there are not many benefits to buying the phone from your carrier versus buying it from a third party vendor.  In the end, it will come down to what is most convenient and where you can find the best deal.  Carriers often do offer a warranty on refurbished phones, but there are some third parties that do the same.  Keep in mind that you may be able to find a better deal on used AT&T cell phones from other places than the local AT&T store.

On the other hand, most cell phones that are purchased directly from a cellular service provider are locked to that particular network, meaning those phones cannot be activated on any other networks.  Unlocked a phone is often a simple process, but does take time and effort on your part.  The alternative is to purchase an unlocked cell phone directly from a third party vendor.

Another perk to purchasing your used cell phone from your carrier is that they will often offer bundle packs. These bundle packs will include several accessories that you might otherwise have to pay around $100 for! A Bluetooth headset, car charger, and carrying case specifically for your used phone.