Swiss steak is a braised beef dish. Despite the name, "Swiss" has nothing to do with Switzerland; it refers to swissing, a term borrowed from a 19th-century fabric-pressing process, describing the pounding or rolling used to tenderize the meat.
A tough cut, such as round steak or chuck, is pounded or rolled to break down muscle fibers, then coated in flour, seasoned, and browned. Onions, tomatoes, and other vegetables are added, and the dish is simmered for 1-2 hours; the acidity in the tomatoes also helps break down connective tissue.
It's a classic American home-cooking dish, especially in the Midwest and South, usually served over mashed potatoes, rice, or noodles to soak up the sauce. Common variations add mushrooms, bell peppers, Worcestershire sauce, or red wine.