Fat back, a.k.a. fatback, is, much as it sounds, the fat from the back of a pig. It is a "hard fat" that can be chopped and ground. As such, fat back is a key ingredient in sausages to add flavor and juiciness. Although it's solid at room temperature, it is easier to chop or grind if it's been well chilled - even a quick 15-minute stop in the freezer can help it keep its shape as you work with it, especially when grinding sausage.
Fat back can be added to any dish using ground meat for additional flavor and moisture. Note, however, that fat back has a rather high water content. This can aid in a juicy factor, but it can also cause shrinkage in items like burgers or meat loaves if too much fat back is used or the dish is overcooked.
While fat back can be rendered into lard, the result is less prized than the more delicate leaf lard rendered from the "soft fat" that comes from the abdominal cavity.
Fat back is also sometimes used to refer to salt pork. True salt pork is fat back that has been salted and cured to prolong its shelf-life. Salt pork is an important ingredient in southern cooking, adding flavor and juiciness to greens and other dishes. It was also a standard provision in pioneer larders in the 19th century, since it was relatively cheap, kept well, added flavor to meals, and provided an easily portable cooking fat.