The Dow Jones Industrial Average (DJI), commonly just referred to as "The Dow", is an average of the price of 30 stocks. The stocks represent 30 of the largest and most widely traded stocks in the United States. The Dow Jones Corporation, the administrators of the index, changes the stocks in the index from time to time. On November 22, 2002, the following 30 stocks were components of the index:
3M, Alcoa, American Express, AT&T, Boeing, Caterpillar, Citigroup, Coca-Cola, E.I. DuPont de Nemours, Eastman Kodak, Exxon Mobil, General Electric, General Motors, Hewlett-Packard, Home Depot, Honeywell, Intel, IBM, International Paper, J.P. Morgan Chase, Johnson & Johnson, McDonald's, Merck & Co., Microsoft, Philip Morris, Procter & Gamble, SBC Communications, United Technologies, Wal-Mart, and Walt Disney.
The Dow Jones Industrial Average is computed by taking the average price of the 30 stocks and dividing that figure by a number called the divisor. The divisor is there to take into account stock splits and mergers. Otherwise the index would decrease whenever a stock split took place. Suppose a stock on the index worth $100 splits is split or divided into two stocks each worth $50. If we did not take into account that there are twice as many shares in that company as before the DJI would be $50 lower than before the stock split because one share is now worth $50 instead of $100.
The divisor is determined by weights placed on all the stocks (due to these mergers and acquisitions) and changes quite often; at November 22, 2002 the divisor was equal to 0.14585278. So if you took the average cost of each of these stocks on November 22 and divided this number by 0.14585278, you'd get the closing value of the DJI on that date which was 8804.84. You can also use this divisor to see how an individual stock influences the average. If the price of International Paper increases by two points, the DJI would increase by 13.7 points assuming none of the other stock values changed (13.7 = 2 / 0.14585278). Because of the formula used by the Dow a one point increase or decrease by any stock will have the same affect, which is not the case for all indices.
So the Dow Jones number you hear in the news each night is simply this weighted average of stock prices. Because of this, the Dow Jones Industrial Average should just be considered a price in itself. So when you hear that the Dow Jones went up 35 points, it just means that to buy these stocks (taking into account the divisor) at 4:00pm today (the closing time of the market) it would have cost 35 more dollars than it would have cost to buy the stocks the day before at the same time. That's all there is to it.