Gascony is a region in far southwestern France. Its south side borders Spain; its west side is on the Atlantic coast. 
It used to be more or less a defined political region, but since the French revolution the area has been parcelled out amongst different political “départements.”
Still, it exists in terms of French culture and food as a defined region, in the same way you’d refer to “New England” cooking, even though that region spans several American states. The adjective in English to describe things from or of Gascony is “Gascon.”
The Gascony area is very rural, with country style cooking.
Goose, duck and pork are prominent meats, leading to the three main cooking fats being goose, duck and pork fat.
The area is well-known for several foods: Foie Gras, Confit d’Oie (pieces of geese potted in goose fat), its prunes (particularly the “Pruneau d’Agen”), jambon de Bayonne (“Bayonne ham”), as well as dishes such as “Garbure” (cabbage and bacon stew.)
The most well-known alcohol produced in the region is the brandy called “Armagnac.” It’s named after the historical area of Armagnac in Gascony, bordered by the Adour River to the south, and the Garonne River to the north. This Armagnac area now roughly corresponds to the département of Gers. Owing to the prominence of the brandy, Gascon dishes will often call for meats marinated first in Armagnac.
The cooking draws particularly on flavourings from herbs, mushrooms, cloves, leeks, shallots, onions and garlic.
As well, there is a mixture called “quatre épices” (“four spices”), made from cinnamon, cloves, ginger and nutmeg. The mixture actually also includes pepper, so it really ought to be called five spices, but in Gascony any spice mix always includes pepper, so its presence is just taken for granted. This mixture goes well with dark meats like goose and duck.
Literature & Lore
D’Artagnan in the book “Three Musketeers” by Alexandre Dumas was from Gascony (according to the book.) The character was based on Charles de Batz from Auch (pronounced Osh), born 1611. In the play, Cyrano de Bergerac, the hero Cyrano is from Gascony.
 Some travel maps will draw the region differently. It all depends which historical period they lean the heaviest on, and there is a wide choice: the region dates back to the Roman province of “Novempopulania.”
Davis, William A. Gascony, France: Flavorful experiences are on the menu at Camont’s cooking school. Los Angeles, California, USA: Los Angeles Times. 2 May 2010.
O’Neill,Molly. The Duck Stops Here. New York Times. 8 November 1992.
Pacult, Paul F. Pairings: A Taste of Gascony. Wine Enthusiast Magazine. 1 January 2007.