There are many different types of indexes in the stock market. For instance, we have the Dow, Nasdaq, S&P and others; the three mentioned are the most famous. Different countries have their own stock markets as well. These charts are supposed to represent stocks in general. So, the Dow follows thirty blue chip companies (IBM, Home Depot, J P Morgan Chase, for example). The idea behind this is simple: if the Dow is up, then it is a good gauge that the rest of the stock would be up as well. The Nasdaq is more reflective of technology stocks. In short, the points on the stock market represent the level at which the companies that are in that particular index is measured.
Investive, this is a very good question. With the economic turmoil of late, it is more important than ever to understand the ins and outs of the stock market.
First of all, 1 point on the U.S. stock market is equal to 1 U.S. dollar. For example, if stock in a certain company is down by 10 points, that is equivalent to ten dollars. The Down Jones Industrial Average is a cumulative number that represents the stocks of 30 large U.S. companies that are considered to be good indicators of the market's overall health. Thus, when the Dow Jones Industrial Average takes a sharp downtown, or a sudden upturn, we can use it to hypothesize about the overall state of the economy.
To clarify the term "stock", a stock can be defined as a share held in a company by an individual. A stock may be purchased for a given price based on market speculation, and then sold for either a profit or a loss. When the Dow Jones Average plummets, stocks in the 30 companies have also fallen.
I hope this helps!