What Exactly is "The Market"?

Today the stock market was up or down. Watching the national news today, you may see a graphic showing the Dow Jones Industrial Average was up 6.74 points to 12,239.89. This keeps some sort of streak going (8 up days in a row) that will also be worth commenting on. However, many professional investors are benchmarked to the S&P 500 Index. If this is your definition of the market then it was down on the day. The S&P 500 Index closed down 3.69 points to 1320.88. So like many things in life, two people may look at the stock market today and see two completely different things. One will say it was up and another will say it was down.