The term "barbecue" is used loosely. Barbacoa is not a method of grilling something over an open flame. Traditional Mexican barbacoa is completely different. It essentially steams and smokes the meat at the same time resulting in a moist and flavorful meat.
First, the head of a cow or goat meat is wrapped in maguey or banana leaves.
A cauldron of hot water is placed in a pit about 3 feet deep with hot coals in the bottom. A grill is placed on top of the cauldron and the meat is placed there. Vegetables, beans and spices are sometimes added to the pot for a soup. The pit is then sealed and covered with damp earth.
Traditionally, the type of meat used is from the head of the cow. Lamb or pork is also used.
Nowadays "barbacoa" can refer to meat that is just slow cooked and tender.