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WIkipedia: Burrito
A burrito (IPA: /bəˈriːto/), or taco de harina, is a type of food found in Mexican and Tex-Mex cuisine. It consists of a flour tortilla wrapped or folded around a filling. The flour tortilla is usually lightly grilled or steamed, to soften it and make it more pliable. In Mexico, refried beans, Mexican rice, or meat are usually the only fillings and the tortilla is smaller in size. In the United States, however, fillings generally include a combination of ingredients such as Mexican rice, beans, lettuce, salsa, meat, guacamole, cheese, and sour cream, and the size varies, with some burritos considerably larger than their Mexican counterparts.

The word burrito literally means “little donkey” in Spanish, coming from burro, which means “donkey”. The name burrito possibly derives from the appearance of a rolled up wheat tortilla, which vaguely resembles the ear of its namesake animal, or from bedrolls and packs that donkeys carried. It is similar to the taco.
 
History
Mexican popular tradition tells the story of a man named Juan Mendez who used to sell tacos in a street stand, using a donkey as a transport for himself and the food, during the Mexican Revolution period (1910-1921) in the Bella Vista neighborhood in Ciudad Juárez, Chihuahua. To keep the food warm, Juan had the idea of wrapping the food placed in a large home made flour tortilla inside individual napkins. He had a lot of success, and consumers came from other places around the Mexican border looking for the “food of the Burrito,” the word they eventually adopted as the name for these large tacos.
 
Burritos are a traditional food of Ciudad Juárez, a city in the northern Mexican state of Chihuahua, where people buy them at restaurants and roadside stands. Northern Mexican border towns like Villa Ahumada have an established reputation for serving burritos, but they are quite different from the American variety. Authentic Mexican burritos are usually small and thin, with flour tortillas containing only one or two ingredients: some form of meat, potatoes, beans, asadero cheese, chile rajas, or chile relleno. Other types of ingredients may include barbacoa, mole, chopped hot dogs cooked in a tomato and chile sauce, refried beans and cheese, deshebrada, and (shredded slow-cooked flank steak). The deshebrada burrito also has a variation in chile colorado (mild to moderately hot) and salsa verde (very hot). The Mexican burrito may be a northern variation of the traditional “Taco de Canasta.” They are eaten for breakfast, lunch, and dinner.

Although burritos are one of the most popular examples of Mexican cuisine outside of Mexico, in Mexico itself burritos are not common outside of northern Mexico, although they are beginning to appear in some non-traditional venues.

Wheat flour tortillas used in burritos are now often seen through much of Mexico, but at one time were peculiar to northwestern Mexico, the Southwestern US Mexican American community, and Pueblo Indian tribes, possibly due to these areas being less than optimal for growing maize.
 
Burritos are commonly called tacos de harina (wheat flour tacos) in Central and Southern Mexico and burritas (feminine variation, with ‘a’) in northern-style restaurants outside of Northern Mexico proper. A long and thin fried burrito similar to a chimichanga is prepared in the state of Sonora and vicinity and is called a chivichanga.
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Breakfast burrito
Southwestern cuisine, New Mexican cuisine, and Tex-Mex in particular, has popularized the breakfast burrito. An entire American breakfast can be wrapped inside a 15-inch flour tortilla, accompanied by field-fresh, often very hot, green chile. Southwestern breakfast burritos may include scrambled eggs, potatoes, onions, chorizo, guisado, or bacon. Tia Sophia’s, a Mexican café in Santa Fe, New Mexico, claims to have invented the original breakfast burrito in 1975, filling a rolled tortilla with bacon and potatoes, served wet with chili and cheese. Fast food giant, McDonald’s introduced their version in the late 1980s and by the 1990s, more fast food restaurants caught on to the style, with Taco Bell, Sonic, and Carl’s Jr. offering breakfast burritos (smaller in size) on their menus.
 
(Oxford English Dictionary)
burrito
Chiefly U.S.
[Amer. Sp., dim. of burro BURRO, ass.]
A Mexican dish consisting of a maize-flour tortilla rolled round a savoury filling (of beef, chicken, refried beans, etc.).
1934 E. FERGUSSON Mexican Cookbk. 33 Burritos (Little Burros). Mix tortillas..but mold them thicker than usual. Make a depression in the middle of each and fill with chicharrones.
1962 MULVEY & ALVAREZ Good Food from Mexico (rev. ed.) iii. 81 Burritos in the northern part of Mexico and in the southwestern part of the United States are quite different. Now a popular dish in many restaurants and taco stands in California and Texas are northern burritos, which are made by folding a flour tortilla around a mound of re-fried beans, seasoned to taste with chili.
1971 Sunset Jan. 85/1 A burrito party is an excellent way to entertain a few guests.
1978 J. WAMBAUGH Black Marble iv. 35, I got a victim who’ll I.D. anybody I show him. Owns the burrito stand over on Western.
1984 Miami Herald 30 Mar. 14A/3 She ate three tacos and a burrito at lunch.
 
Google Books
Diccionario de Mejicanismos
By Féliz Ramos y Duarte
Second Edition
Mexico City: Herrero Hermanos
1898
Pg. 98:
Burrito (Guan.), sm. Tortilla arrollada, con carne u otra cosa dentro, que en Yucatan llaman cocito, i en Cuernavaca i en Mejico, taco.