Insider trading occurs when a person within a company (or connected to someone within a company) takes information that they have access to and uses it to buy or sell stock. The information used is information that is not available to the general public and which allows the inside trader to get a better deal on their stock transactions than a member of the general public would. Insider trading is illegal and is, in the US, under the jurisdiction of the Securities and Exchange Commission (SEC).
As an example of this, the prominent New York businessman Rajat Gupta has just been charged with insider trading. He is alleged to have learned in a Goldman Sachs board meeting that Warren Buffett would make a big investment in the company, which would lead to the firm's stock price rising. He then called a friend, hedge fund manager Raj Rajaratnam and told him the news whereupon Rajaratnam used the information to buy Goldman Sachs stock while the price was still low. Rajaratnam has already been convicted of insider trading.