If you choose a purchase in which you state it is a gift (This will be a gift order), then you have option to choose gift wrapping or not.
I just bought two Paperwhites as a gift, they still haven't been shipped (neither was my account charged).
I didn't choose the gift wrap (which is charged additionally), so what it stated on Amazon was that kindles will be packed in a box on which there will be no Amazon logo printed (so that it is a surprise) + they allow you to leave a gift note on which you write what you want
