Beef tenderloin is an exceptionally tender cut of beef from the muscle that runs along the spine in the short loin, a muscle that does very little work in the live animal.
Filet mignon is not another name for the whole tenderloin, it's a specific steak cut from the narrow tail end; the thicker center is often cut into chateaubriand, and the rest is sold as tenderloin roasts or medallions.
Tenderloin is prized in fine dining worldwide, from French filet mignon to Italian beef carpaccio and beef Wellington, for its buttery texture and mild flavor. Because the flavor is subtle, it's typically paired with bold sauces (béarnaise, bordelaise, mushroom), aromatic herbs like rosemary and thyme, and acidic elements such as red wine or balsamic vinegar.