The burrito is the baseline that every other entry in this cluster bends away from: a large flour tortilla wrapped completely around a filling, sealed at both ends, eaten in the hand. What defines it is the relationship between a single warm wheat tortilla and a filling chosen to stay put inside it. The tortilla is not bread in any leavened sense. It is a thin, pliable sheet of wheat flour, fat, and water, griddled until it flexes, and its whole job is to be strong enough to contain a wet interior and neutral enough to disappear behind it. The filling supplies flavor and moisture; the tortilla supplies hold and structure. Take away the wrap and you have a plate of stew; take away the filling and you have a folded blank. In the Northern Mexican reading the contents are spare, often a single braised meat or a bean, and the discipline is in restraint. The American reading, which traveled north and grew, loads rice, beans, cheese, and more into a much larger cylinder. Both are the same idea executed at different scales.
A good burrito begins with the tortilla, which should be fresh, soft, and warmed on a comal or dry griddle until it turns supple rather than brittle. A cold tortilla cracks at the fold and the burrito fails before the first bite. The filling has to be moist enough to be pleasant but not so loose that it pools, so a braise is usually drained of excess liquid and a wet sauce is bound by something starchy. The wrap itself is a technique: filling kept to a tight core well short of the edges, the bottom flap folded up over it, both sides tucked in, then the whole thing rolled forward firm and tight so the tortilla compresses the contents rather than draping over them. A sloppy build leaves slack tortilla, an unsealed end, and a filling that escapes from the back as you eat. A good build is a dense, even cylinder that eats clean from one end to the other.
The variations are largely a question of what goes inside the same wrap. Swap in grilled beef and you have a burrito de carne asada; braise pork in a tomatillo sauce and you have a burrito de chile verde; fill it with eggs and potatoes and it becomes a breakfast burrito. Hold the contents constant and shrink the format toward an open single tortilla and you drift toward the taco, a different structure entirely. Wrap the same filling, then batter and deep-fry the whole thing, and the cousin is a chimichanga, crisp-shelled and built on different physics, which deserves its own article rather than being crowded in here.