Replacement devices are 'service units'. They may be new (not in retail packaging), or they may be remanufactured. There is no way for you or anyone at your local Apple Store to tell the difference. They do not use repaired failed quality control devices.

Does Apple replace iPhones with new ones?

Your replacement iPhone will be new or equivalent to new. Issues caused by accidental damage aren't covered under the Apple Limited Warranty.

What does replaced iPhone mean?

It means that it is a refurbished device ( most of the time) and it look brand new, If the iPhone you turn in to Apple is sim locked to a provider the replacement device will also be locked.