Flat iron steak is a steak taken from one of the muscles in the beef chuck primal cut, specifically the top blade (or infraspinatus) muscle, which is part of a muscle group called the chuck shoulder clod.
Also see: Beef Cuts Diagram
If you know anything about beef chuck, you know that it comes from one of the most heavily exercised parts of the cow, and it has a lot of tough connective tissue in it.
However, the top blade muscle is actually pretty tender. The only problem with it is that it has a long strip of sinew running through it, which gets tough and chewy when cooked over high heat.
The solution is to slice the muscle lengthwise, just above that strip of gristle, and then flip it over and do the same to the other side. If you imagine the way you might fillet a fish, that's the way a flat iron steak is created from the top blade.
There's a certain amount of skill involved in this, mainly so that all of the gristle is removed without leaving too much meat attached. The leftover trimmings usually end up being made into ground beef.
Also see: What is a Delmonico Steak?
Dividing the top blade muscle in this way produces two long strips of tender, flavorful, well-marbled beef which can be portioned into individual steaks called flat iron steaks.
Note that the top blade muscle also happens to be the same one from which we get beef blade steaks, with the only difference being that it's sliced crosswise rather than lengthwise. Thus, each blade steak has a piece of tough gristle in it, making it more suitable for braising than grilling.
Another interesting thing about the flat iron steak is the way its increasing popularity has indirectly given rise to the existence of all kinds of other steaks and roasts from the beef chuck, simply because once the top blade muscle is removed, a butcher can't make that beef chuck into traditional chuck roasts anymore.
What's left can go into the grinder, but that isn't very profitable. What ends up happening is that the whole beef chuck gets pulled apart, muscle by muscle, and sold as steaks and roasts — of varying quality. If you're interested, you can read a lot more about the beef chuck primal cut.