Refurbished means it's been gone over by a technician who checked everything he could. (Refurbishing is a nice job - you get to play with lots of phones, and you can always tell the boss "I was just checking the doodad", as long as you put out enough phones a day.) The tech will usually catch things the computer in the factory will miss on a new phone (like your camera problem).
Most refurbs are phones returned by a customer after a day or so because they prefer a different phone - there's nothing wrong with the phone. (Phones with problems are either fixed on the spot or become electronic scrap. Labor is more expensive than replacing the phone.) You're giving them a used phone and getting an almost new one (effectively a new one) in return.
I'm on my 3rd Note 3. The first one bricked during an update the day after I bought it, so they replaced it with a new one. That one blew some storage a few weeks later, so they replaced it with a refurb - 19 months ago. I still get 2 days on a charge. I have no problem with a refurb. (And I was in the business for a while, so I know the difference between a refurb and a used phone. TMobile in the US gives you a refurb.)