Perfect, whole Star Anise are a beautiful wonder of nature. Each of the eight points contains a single glossy seed, for a gorgeous flower shape that makes a dramatic presentation when floated in tea or soup. Being picked out by hand makes them more expensive, and they are often used for crafts and sometimes as an attractive dinner garnish. For nearly all culinary uses where the appearance of the anise isn't important, the broken or powdered star anise are a much cheaper way to get the same flavor.
Star anise is also known as Chinese anise, and features the same three essential oils as the botanically unrelated anise seed. Waverly Root writes, "In putting this combination together once nature had already amply demonstrated her chemical skill; it was sheer showing off to perform the feat twice in two totally unrelated plants." The flavor is noticeably more intense than the anise seed and is used primarily for Chinese cooking, although in the 1700's European cooking also called for star anise in fruit jams and syrup recipes.