Matignon is a vegetable mixturethat's cooked down to a pulp - or fondue, as it is called in French. Veggies - carrots, onion, and celery are cooked slowly in butter with seasons, salt, bay leaf, thyme, and sugar. Once the vegetables are soft, Madeira is added to the mixture, and then it is cooked further until all the liquid is evaporated. This process produces a Matignon au maigre (veggie version), or it could be au gras (with bacon).
Once you have made the Matignon, it can be added to other dishes. For instance, it may be spread on beef or chicken fillet that's been braised, or chicken can be roasted on a bed of Matignon. Once the meal is served, the Matignon may be added to the dish as a garnish.
In restaurants, Matignon may be referred to as an edible mirepoix. This is a mixture of carrots, onion, and celery (or leeks) with herbs that flavors stock, stews, and soup. In this case, Matignon won't be added to the finished dish.
Matignon may also be a side dish with stuffed artichoke hearts, browned and sprinkled with bread crumbs. This dish is served with port wine sauce and braised lettuce.