Pork sausage is made by grinding pork meat with fat, salt and other seasononings (as well as preservative and fillers in some cases). It can be sold in bulk, as patties, or, as is most common, packed into a casing to form links.
There are myriad kinds of pork sausages (and, indeed most sausages are made form pork, though there are veal, chicken, and even seafood sausages as well). Pork sausage can be fresh (like Italian sausage), cooked (like hot dogs); smoked (like Andouille); or cured and dried (like salami). All are enjoyed differently. In cooking, a good recipe will specify which kind of pork sausage is called for.
Sausage made from other meats can be substituted but flavor and texture may vary; chicken sausage, for example, is far more lean.