The appearance of the navel depends on how the cord was cut and also on the condition of the underlying muscle. If the muscles are firm and the cut was close enough to the belly, the navel will go inward. If the muscles are weak and/or the cut was too far from the belly, the navel will protrude outward.
The word navel came from the Anglo-Saxon "nafe" for the hub of a wheel. Also called the belly button.