Combat sports are the best example of all that makes humans great. They show intelligence, tactics, will power and desire. They show the peak of human physical conditioning and training.
They are not battles of thugs, but men of equal skill that are really battling with strategy and will. Testing the peaks of mental and physical toughness while pushing their desire to achieve to a maximum level. While a good chess match might test the mental strength of the combatants, combat sports take that same depth of strategy and tactics into the physical realm. Learning to use your body to peak efficiency while at the same time working to develop and implement tactics that allow you to work the best in an a established rule system is very awe inspiring.
People watch for many reasons. Some for what I've listed above, some to watch violence and fill that need for danger, some for hero/villain worship, and some just to have an excuse to go to the bar.