Refurbished models have the same warranty, same eligibility for AppleCare, etc.
A refurbished unit is tested and certified to work as new (and possibly might be less likely to fail than a new unit since early burn in is done, and it has to have a complete assessment prior to resale).
Some buyers return Macs for no good reason at all, and those units go into the refurbished pool; Apple cant sell them as new. Refurbished units are not beaten-up stuff, though they might have a minor scratch on a case (for example). But in my experience they look just like new.
Remember that new or refurbished, there is always some failure rate; a new unit is no guarantee.