The whole beef brisket is a large cut of meat that is taken from the chest area of the butchered steer. The whole brisket has a large amount of fat, part of it internal and the rest found as a layer on one side. A good brisket will have fat marbled throughout the meat, which helps keep the beef tender and juicy.
Brisket also contains quite a bit of connective tissue because the two muscles of the brisket are worked whenever the steer walks around.
The connective tissues make the brisket tough if it's not cooked long enough to break them down. Smoking for hours at relatively low temperatures is a great way to do that. And when the connective tissue softens and melts, it adds rich flavor to the meat and makes it nice and juicy!
The brisket you see below consists of the flat and the point, which are separated by a pocket of fat. There is a layer of fat on one side of the brisket which can vary in thickness.
Still looking at the above picture, the layer of meat you see on top is the brisket flat. You can't see it in this picture, but laying under the flat on the left side is the point, which is the second muscle in a whole brisket. In the next picture the point is a little easier to see.
On the right end you can see where the grain direction of the meat changes. That's the point. There's also a narrow vertical line of fat separating the two muscles.
In this picture you can see the layer of fat covering the top side. That's called the fat cap. On the left end, the meat you can see showing through the fat is part of the point peeking out.
The brisket point is the more tender section of the whole beef brisket. It contains a bit more internal marbling than the flat, and less connective tissue.
When the brisket is all cut up and laying on the serving platter, that's the part that disappears the quickest!