If you own more than one cat, you may already be aware that domestic cats have a very developed sense of pecking-order. One cat will tend to be the leader of the pack, the aggressive, domineering one, while the others will be more submissive. The one who runs the show is called the alpha cat by people who study animal behavior.
When the alpha cat is out of the room, the beta cats may tussle among themselves for a secondary kind of dominance. Beta cats will also tussle with the alpha cat, but it's usually pretty clear who's the big boss, even if she or he has to knock around the contenders every now and again.
Cat owners tend to be all too aware of which cat is the alpha in their house. If you are uncertain, though, there are some easily-discerned signals that cats use among themselves to announce their status. With a little practice you can spot them communicating in all sorts of subtle ways we humans might not ever notice. For example, watch the tail.
When walking around, the alpha cat will hold her or his tail higher in the air than the betas. It acts as a flag that says: "Right here. Fonzie Fonzarelli. Mr. Big Man on Campus." Beta cats will also hold their tails up, but not as high as the alpha, unless they want to risk a fight.
If this seems like a terribly subtle way to communicate dominance to you, try and substitute a human behavior. When someone stares at you for even a second or two, you get the message!