A technique by which part of one animal is stuffed inside another animal. The resulting food is then cooked. The most famous example and application of this technique is the turducken.
The technique itself can be traced back to the Middle Ages. Though it is difficult to say with certainty that this is the first instance in Europe, one of the earliest uses was for a dish called cockentrice. In that dish, a capon (castrated rooster) is stuffed into a pig. However, it wouldn’t be until the advent of the 18th and 19th centuries that engastration would hit it strides with the mainstream culture.
Indeed, some reports of the era, most notably Alexandre Balthazar Laurent Grimod de la Reynière (basically the proto-“foodie” during Napoleon’s reign) speak of roasted birds that have been stuffed via engastration. There are plenty more dishes to speak of, most of them savory in flavor. However, modern use cases of the term have been extended to non-animal based uses, even going so far as to apply the term to desserts.