The Dow is a list, or index, of companies considered to be good indicators of the market's strength. Simply put, these companies are a barometer of the market: when they do well, the economy is doing well, and vice versa. So the Dow takes the average value of these companies every day to see if it has increased or decreased.
Because the index is dealing with companies that are worth billions of dollars, a simple method of displaying their changes in value had to be formulated. The clever and resourceful Charles Dow broke everything into points rather than dollars. The points still represent dollars, but the ratio is not 1:1. This way, instead of saying, "Today, the Dow stocks collectively gained $693.573961, give or take a few thousandths," people can say, "The Dow was up 100 points." Obviously, this is a vast improvement.
However, because the Dow only consists of 30 different stocks, it is not the best representation of the entire market. Sometimes investors are misled into believing that if the Dow is up, so are all other equities, but this is not the case.
(To learn more, see: Calculating the Dow Jones Industrial Average.)