The secondary market is where most investors do the lion's share of their buying and selling of stocks. The New York Stock Exchange, AMEX, Nasdaq, and other major exchanges across the globe are secondary markets.
The best way to understand what the secondary market is, is to understand what it is not. For stocks, primary markets are where buyers purchase a company's shares directly from the company, such as during an initial public offering, or IPO. In the secondary market, owners of stocks are trading among themselves. When you buy stock in the secondary market, the money goes to the owner of the stock, not to the company.
A secondary market can be an auction market or a dealer market. In an auction market, individual buyers and sellers (or their brokers) come together and bid to buy or sell stocks. "Specialists" match up buyers and sellers. This process establishes the market value for an asset via a bid/ask auction system.
In a dealer market, dealers trade from their own accounts at firm bid and ask prices, using their own research and expertise.
Trading in the secondary market establishes a company's market capitalization. Multiply the price of one share of stock by the number of shares outstanding and you end up with what the market thinks a company is worth. Market cap is important, but many things unrelated to the fundamental strength or weakness of a business can affect it.
The number of shares traded in a day (market volume) also tells investors something about whether a company's stock is in demand. Big fluctuations in volume could indicate changes at the company or how it is perceived. You also want to consider volume on the secondary market when looking at what is causing price changes.
Secondary markets are also the place where packaged investments such as collateralized debt obligations are offered for sale. It's also where companies go when they issue additional stock to raise money via a secondary offering.