Andouille (pronounced "ahn-DOO-ee") is a spicy sausage made from smoked pork. Andouille sausage is thought to have originated in France or Germany, a pair of countries that both have rich and extensive traditions of sausage making (or charcuterie, as it is known in French).
Indeed, andouille is a mainstay of Cajun cuisine, which traces its roots to Canadian immigrants of French origin, and also Creole, which represents a highly eclectic mixture of French, Spanish, German, West African and Native American influences.
Thus, today andouille sausage is associated with the cuisine of Louisiana, which is the center of the U.S.'s vibrant Cajun and Creole communities.
Traditionally, French andouille was (and still is) made by utilizing the entire digestive tract of a single pig. To be specific, the filling consisted of the animals stomach and small intestines (i.e. chitterlings), chopped or sliced into strips, combined with onions and seasonings in a casing made from the animal's large intestine.
It is thus quite a large sausage, and not prepared using smoke but rather poached, then allowed to cool and served cold in thin slices. They can also be grilled.
A smaller version, made using the small intestine as casing, is called andouillettes, and is often grilled and served with mashed potatoes.
In the U.S., andouille sausage is made with pork butt, and if all this talk of the pig's intestines and digestive tract has got you spooked, I can assure you that the term pork butt in fact refers to the upper shoulder of the animal, and sometimes goes by the name Boston butt.
Andouille in the U.S. is highly spiced, particularly the Cajun version, and it generally undergoes two rounds of smoking: first, the meat to be used as filling is smoked, and then the finished sausages are smoked yet again.
Sliced andouille sausage is one of the key ingredients in traditional Cajun dishes such as gumbo and jambalaya (as well as the Creole versions).
If you're making something like gumbo or jambalaya and you can't get your hands on true andouille sausage, you can substitute any smoked pork sausage, but your best options will be Spanish chorizo, if you can find that, because it is similarly spiced.
Failing that, any smoked or air-dried sausage will do, and in a pinch you can certainly use kielbasa. But in general, the drier the sausage, the better. You want your sausage to more closely resemble jerky than the fresh, juicy sausages you see in the butcher case.