For a word that doesn’t come up very often, it has a surprising number of meanings. It comes up in French cooking, and at its most basic is a vegetable mixture that has been cooked down to a pulp. Only the French don’t call it a pulp, they call it a fondue, which simply means "melted."
Carrots, celery, and onion are cooked very slowly in butter, with a little salt, thyme, bay leaf, and sugar. When the vegetables are already very soft, some Madeira is added, and cooked further until almost all of the liquid has evaporated. That produces a maitgnon au maigre, or vegetarian version. It can also be prepared au gras, with the addition of a little bacon.
The matignon is then used as an ingredient in other dishes. A chicken might be roasted on a bed of matignon in a covered dish in the oven, or the matignon can be spread on a chicken or a beef fillet that is to be braised. When the meat is done, the matignon is collected and served as a garnish.
Matignon is also the name of a side dish, in which artichoke hearts are stuffed with the vegetable pulp, sprinkled with bread crumbs, and browned. These are served with braised lettuce and a port wine sauce.
In restaurant kitchens in this country, matignon is sometimes referred to as an edible mirepoix. A mirepoix is a mixture of diced carrot, celery, and onion (or leek), with some herbs that is used to flavor stocks, soups and stews, and often does not make it into the finished dish. A matignon in this country generally includes some ham.