Refurbished is the description of products (usually electronics) that have been previously returned to a manufacturer or vendor for various reasons. Refurbished products are normally tested for functionality and defects before they are sold, and thus are the approximate equivalent of certified pre-owned cars.
The main difference between "refurbished" and "used" products is that refurbished products have been tested and verified to function properly, and are thus free of defects, while "used" products may or may not be defective. Refurbished products may be unused customer returns that are essentially "new" items, or they may be defective products that were returned under warranty, and resold by the manufacturer after repairing the defects and ensuring proper function.
The phone was returned to the factory because their was a problem, OR the phone did not pass Apple's initial quality control and was "remanufactured" or 'refurbished'. The warranty remains the same as a new one. HOwever, I don't believe you can get an extended warranty beyond 2 years...not sure of this statement but it is easy to validate at 'check out'.