When a cook needs to butterfly a cut of meat, it usually means the piece is too thick to cook properly without drying. To prepare a pork chop in this way, for example, the cook takes a sharp knife and carefully slits the meat halfway through the thickness, almost cutting it through. He then "unfolds" the meat into what looks like a butterfly shape, exposing most of the chop to the heat. Any kind of thick meat cut can be butterflied, including chicken breast or thigh, lamb chop, steak — even seafood. The meat must be thick enough to slice nearly in half, with two fairly thick sides coming from it.
When a cook cuts the chop into this distinctive shape, he is allowing the chop to cook thoroughly and evenly, without drying the meat. The method is generally used on boneless cuts of meat, so the meat can lie flat in the pan or broiler. This method also allows the cook to check the meat more accurately for doneness.
The butterfly technique probably came from France, as most such culinary techniques have. One can imagine King Louis XIV being served porc avec herbes de Provence a la papillon. These kinds of culinary solutions were popularized by the chef Francois Pierre La Varenne in his 1651 Le Cuisinier Francois.
Another advantage of preparing meat in this way is that it allows the cook to brown all sides of the piece, then fold a stuffing into the crease, seal the meat with a toothpick or kitchen string, and cook it with the stuffing mixture inside. Chicken Kiev, for instance, is made in much this way. The chicken breast is butterflied, and a chunk of herbed butter is placed inside the crease. The breast is then rolled up and secured, breaded lightly, and baked. When the diner cuts into the middle of the chicken, the melted butter and herbs pour out on to the plate. Chicken Cordon Bleu uses the same method.
Learning to butterfly a thick cut of meat is a useful culinary skill, and most cooks will want to learn how to do it properly.