Gastrique is caramelized sugar, deglazed with vinegar, used as a flavoring for sauces.
To this a little pends (browned bits or drippings from meats or vegetables, found on the bottom of a sauté or roasting pan via the Maillard reaction) or stock may be added. It is used to flavor sauces such as tomato sauce, savory fruit sauces, and other sweet and sour sauces such as the classic orange sauce for duck à l'orange.
Nowadays the term is frequently used to refer to any flavored sauce, e.g. citrus gastrique, mango gastrique.
An agrodolce (sweet and sour) is a similar sauce found in Italian cuisine.