Description of the Orange Fruit. The orange fruit is one of the most widely consumed fruits in the Unites States. It is a member of the citrus family along with lemons, limes and grapefruit. Oranges are most often covered in a thick, orangey-yellow skin, and the inside is divided into segments of juicy pulp.Oranges are an excellent source of vitamin C. They are also a very good source of dietary fiber.