The word burrito means little donkey in Spanish, as a diminutive form of burro, or donkey. The name burrito as applied to the dish possibly derives from the appearance of bedrolls and packs that donkeys carried.t has been said that to San Diegans, carne asada burritos are as integral to the experience of the place as a slice of pie is to a New Yorker.. The San-Diego style carne asada burrito is served with chunks of carne asada, guacamole, and pico de gallo salsa.