In the culinary arts, the term Delmonico steak can mean a lot of things, and there is little agreement about exactly what sort of steak a Delmonico steak is. In fact, about the only thing people seem to agree on is that it's named for Delmonico's, a steak house in New York where it's said to originate.
[Also see: What is the Best Steak?]
Unfortunately, no one can say for sure exactly what cut of meat Delmonico's was serving when it created the Delmonico steak, because it happened in around 1840, and there's no one around who remembers.
As such, butchers, chefs and steak aficionados can't even agree on whether a Delmonico steak should be boneless or bone-in. And there's even less agreement about precisely what cut of meat it should be made from.
At its most basic, though, a Delmonico steak is a big steak — possibly up to two inches thick. And it should be a very high-quality piece of meat, with plenty of marbling.
Furthermore, it needs come from somewhere in the rib or short loin section of the beef. It might be a bone-in or boneless ribeye or rib steak, or a boneless or bone-in strip steak. Some descriptions of the Delmonico steak depict it as a smaller version of a T-bone steak.
So, we have a mystery. We do know that the Delmonico is a tender cut of meat, which should be cooked quickly with dry-heat cooking methods such as grilling and broiling. (Also see: How to Cook a Steak.)
Ultimately, the Delmonico steak is as much myth as it is a specific cut of steak. Basically, if it's a thick, good quality steak from the rib or short loin, you could call it a Delmonico.
For what it's worth, Delmonico's Restaurant is still in business, and on their menu, the Delmonico steak is a boneless ribeye.
Also see: Cuts of Beef and Beef Diagram