Well, the simple answer is a combination of onions, celery, either the common pascal celery or celeriac and carrots. Mirepoix is a flavor base used widely in stocks, soups, stews and sauces. These ingredients are also known as aromatics. Traditionally, the ratio of these ingredients is 2-1-1, that is, 2 parts onion, 1 part celery and 1 part carrot. And if you want a white stock, or fond blanc, substitute parsnips for the carrots to maintain the pale color. There. I have added one variation. There are many and we will get to that in time.
OK. So where did this come from? Wikipedia says that,

Though the cooking technique is probably older, the term mirepoix dates from the 18th century and derives, as do many other appellations in French cuisine, from the aristocratic employer of the cook credited with establishing and stabilizing it: in this case, Charles-Pierre-Gaston François de Lévis, duc de Lévis-Mirepoix (1699–1757), French field marshal and ambassador and a member of the noble family of Lévis, lords of Mirepoix in Languedoc since the 11th century. According to Pierre Larousse (quoted in the Oxford Companion to Food), the unfortunate Duke of Mirepoix was “an incompetent and mediocre individual. . . who owed his vast fortune to the affection Louis XV felt toward his wife and who had but one claim to fame: he gave his name to a sauce made of all kinds of meat and a variety of seasonings”: The term is not encountered regularly in French culinary texts until the 19th century, so it is difficult to know what a dish à la mirepoix was like in 18th-century France. Beauvilliers, for instance, in 1814, gives a short recipe for a Sauce à la Mirepoix which is a buttery, wine-laced stock garnished with an aromatic mixture of carrots, onions, and a bouquet garni. Carême, in the 1830s, gives a similar recipe, calling it simply Mire-poix; and, by the mid-19th century, Gouffé refers to a mirepoix as “a term in use for such a long time that I do not hesitate to use it here”. His mirepoix is listed among essences and, indeed, is a meaty concoction (laced with two bottles of Madeira!), which, like all other essences, was used to enrich many a classic sauce. By the end of the 19th century, the mirepoix had taken on its modern meaning and Joseph Favre in his Dictionnaire universel de cuisine (c. 1895, reprinted 1978) uses the term to describe a mixture of ham, carrots, onions, and herbs used as an aromatic condiment when making sauces or braising meat.

OK. That’s great. But what is the Cajun variation? Here, from Wikipedia, we find one explanation.

The holy trinity, Cajun holy trinity, or holy trinity of Cajun cooking is the Cajun and Louisiana Creole variant of mirepoix: onions, bell peppers, and celery in roughly equal quantities. This mirepoix is the base for much of the cooking in the regional cuisines of Louisiana. Variants use garlic, parsley, or shallots for one of the three. The preparation of Cajun/Creole dishes such as étouffée, gumbo, and jambalaya all start from this base. Origin of the name – The name is an allusion to the Christian doctrine of the Trinity. Louisiana is a strongly Roman Catholic region. The term is first attested in 1981 and was probably popularized by Paul Prudhomme.

And here are some other variations, mostly from Wikipedia. Enjoy!

1. Not to be confused with Italian Soffritto, which is a kind of Mirepoix. Sofrito being prepared in Spain. Sofrito or refogado is a sauce used as a base in Spanish, Portuguese, and Latin American cooking. Preparations may vary, but it typically consists of aromatic ingredients cut into small pieces and sauteed or braised in cooking oil.
   In Spanish cuisine, sofrito consists of garlic, onion, paprika, peppers, and tomatoes cooked in olive oil. This is known as refogado or sometimes as estrugido in Portuguese-speaking nations, where only onions and olive oil are often essential, garlic and bay laurel leaves being the other most common ingredients.
2. Italian Soffritto. The Italian version of mirepoix is called soffritto (not to be confused with the Spanish sofrito). According to the American reference work The Joy of Cooking, an Italian soffritto is made with olive oil, especially in Southern Italy, rather than butter, as in France or in Northern Italy, and may also contain garlic, shallot, leek, and herbs. From Tuscany in central Italy, restaurateur Benedetta Vitali writes that soffritto means “underfried”, describing it as: “a preparation of lightly browned minced vegetables, not a dish by itself.” It is the foundation on which many Tuscan sauces, and other dishes are built. At one time it was called “false ragout”, because soffritto was thought to vaguely recall the flavor of meat sauce…According to Vitali, mastery of the soffritto is the key to an understanding of Tuscan cooking. Her classically restrained Tuscan soffritto is garlic-less and simply calls for a red onion, a carrot, and a stalk of celery—all finely minced by hand and slowly and carefully sauteed in virgin olive oil in a heavy pan until the mixture reaches a state of browning appropriate to its intended use.
3. German Suppengrün. Suppengrün means soup greens in German, and the Dutch equivalent is soepgroente. Soup greens usually come in a bundle and consists of a leek, a carrot and a piece of celeriac. It may also contain parsley, thyme, celery leaves, rutabaga, parsley root and onions. The mix depends on regional traditions as well as individual recipes. The vegetables used are cold climate roots and bulbs with long shelf lives. Suppengrün act as herbs and impart hearty, strong flavors to the soup or sauce, providing a foil for other strong tasting ingredients such as dried peas and beans or pot roast. Large chunks of vegetables are slow cooked to make flavorful soups and stocks, and are discarded when the vegetables have given up most of their flavor. Finely chopped suppengrün are browned in fat and used as a basis for a finished sauce. The vegetables may also be cooked long enough until they fall apart, and may become part of the sauce or pureed to form the sauce.
4. Polish Włoszczyzna. Włoszczyzna is the Polish word for soup vegetables or greens. The word literally means “Italian stuff” because Queen Bona Sforza, who was Italian and married Polish King Sigismund I the Old in 1518, introduced this concept to Poland. A włoszczyzna may consist of carrots, parsnips or parsley root, celery root or celeriac, leeks and savoy or white cabbage leaves, and sometimes celery leaves and flat-leaf parsley. The most typical, prepackaged combination is celery root, parsley root, carrots and leeks. Włoszczyzna is usually chopped up and boiled to form a flavour base for soups and stews.

And if you are still hungry for information and maybe a recipe or two, try CIA – Professional Cook link. Much information here. Hoipe you enjoyed this article. Good luck with your mirepoix!!