A Chinese concoction which combines several (actually five) spices to make a bewitching pungent mixture. Why five? Because five is the number of elements central to Chinese philosophy. The elements (more properly forces, for they're dynamic, not static) are wood, fire, earth, metal, and water, each of which is associated with a taste or flavour: sour, bitter, sweet, spicy, and salty respectively. Just as Chinese medicine works from the assumption that illness is caused by an imbalance of one force, requiring a cure that restores balance, so too foods that combine the five tastes promote health.
Traditionally, five spice powder contains Szechwan pepper, cinnamon, cloves, fennel seeds, and star anise. Sometimes black peppercorns are substituted for Szechwan pepper, cassia for cinnamon, and licorice for star anise. So too ginger and nutmeg are sometimes added, though properly speaking this would be seven, not five spice powder. Five spice powder mixed with soy sauce is what makes that crispy-skinned roasted duck and pork sold in Chinatown taste so good.
Five spice powder can be found in most Asian markets, but afficionados make their own. Use equal parts of each spice, preferably whole. Toast them in a dry frying pan till aromatic, about 1 or 2 minutes, cool, and grind in a spice grinder, food processor, or mortar and pestle (for Popeye arms) till a fine powder. Store this, as all spices, in an airtight container in a cool, dark, place. Use five spice powder sparingly; it can be overwhelming in flavour.
The mix of flavours in spices is not unique to Chinese cooking. The Thai appreciate that very same mix of five flavours as well; sneff and I discuss that here. There is a Bengali spice mixture of five spices, panch phora, which is sometimes also called five spice powder, though it's quite different from the Chinese one; the good sneff has a recipe here. Then there's a Japanese seven spice powder called shichimi-togarashi which gn0sis has written up here. Wonderful mixtures all. No wonder Asian food has become so popular.