Naval is an adjective meaning of or related to ships, shipping, or the navy. Navel is a noun meaning the mark on the surface of the mammalian abdomen where the umbilical cord was attached during gestation—i.e., the belly button. Navel is also the correct spelling for the sweet orange.
Though the words sound the same (please correct us if this is not true in any variety of English), they are not etymologically related. Naval comes from the Latin navis, meaning ship, while navel has origins in Old English. The navel orange, a fruit developed by humans in the 19th century, was so named due to its lower portion’s resemblance to a human navel.
Examples
For salads, try combinations of leaf lettuce with various citrus fruits, navel oranges in particular. [Montreal Gazette (article now offline)]
The combination of the Castro communists and the Soviets caused the Cuban missile crisis of 1962, and led President Kennedy to declare a naval blockade. [Brantford Expositor]
First, is this a frivolous, navel-gazing fad or can you really earn a living at it? [New York Times]
The naval relics, put in dry dock last month for a month of repairs, occupy only a slice of the vast facility just outside Baltimore. [Los Angeles Times]
Bonds then hiked his shirt, and Anderson injected Bonds in the area of his navel, she said. [San Francisco Chronicle]