The term Apple prefers to use is 'Remanufactured'.
Refurbished has gotten a bad reputation because of defective devices and poor performance. But the thing with Apple is that remanufactured devices get all new casings, brand new batteries and only those parts which do not fail quality testing are replaced.
Once all that's done the device itself is run through a quality control check that is more rigourous than the one they have for new phones. If it fails there they recycle it.
So, essentially you get a phone that is equal to or in some ways superior to a new phone.
The replacement phones I had for my original iPhone 5 were superior to that original phone. The replacement 6+ I had at one point was superior to my original 6+.
That's because those remanufactured devices benefitted from the assembly line adjustments Apple had made by that point.