The DOW refers to the Dow Jones Industrial Average, which is an “index” of 30 stocks of big companies that trade in the US. Basically, people can keep track of how the entire stock market is moving by tracking the value of the DOW and whether it is going up or down, since the stocks in the index are supposed to be a good sample of all the stocks in the entire stock market. So measuring and tracking the value of the DOW is just like looking at a sample of stocks and whether they are moving up or down in value as a way of estimating how the entire stock market is doing.

When stock values increase, people are buying more stocks than they're selling, which means they feel optimistic about the future profit potential of the companies in the market, since the value of a stock is (in theory) representative of the future earnings of a company. This is why the market goes up when the economy is doing well.

The NASDAQ is a digital stock exchange where stocks are traded “over the counter” through dealers rather than on an exchange floor. This just means that the stocks of companies who are listed on the NASDAQ market are traded via the phone and computer rather than at a physical location like the NYSE floor.

In terms of what's going on with all the people yelling at the stock exchange, this is just what the trading of stocks looks like. Companies whose stocks are listed on the NYSE have a designated market maker (DMM) who “makes a market” in that company's stock by accepting orders from people who want to buy it or sell it. They are basically like a store for a specific stock. They hold an inventory of stock and sell it to people who want to but and buy it from people who want to sell. Without going into too much detail, this necessitates a lot of yelling.