a refurbished phone is a phone that was most likely broken before but they fixed it. They are cheaper probably because they have a bigger chance of either breaking again or not working again so I would not reccomend getting a refurbished phone.
Refubished phones are the same phone only it's gone back to the factory to be reinspected and repaired. Normally these will come with the same warranty as a new phone.
I have purchased many refurb phones from AT&T and only had one that had to be returned. It was a quick easy exchange and I got another of the same exact phone that worked perfectly.