Money laundering is defined as a process by which "dirty" money is made to appear as legitimate income. If, say, a drug dealer owns a million dollar home, but hasn't been officially employed at all during his life, how is he going to explain it to the IRS and FBI? The federal agencies are obviously going to do some sort of investigation to find the source of funds. To conceal the illegal source of his income, he must use money laundering.
Money laundering can range from being very complex to very easy, depending on the structure of the organization. In order to make it work, a business has to be involved to make it look like the illegal money is actually money earned by the business. As such, the criminal can take his revenue and claim it as his wage, or even stock dividends in the business. Of course, if the individual is claiming it as legal income, they are forced to pay taxes on it, but at the very least it will give their criminal enterprise a legitimate cover.
Typically, the person receiving the money is the proprietor or primary shareholder of the business. It is usually easiest to set up a business that provides a service, such as an electrician or consulting firm. However, a product distribution business could also be used, although it may be harder to prove that products were actually distributed for the money.
In an easy example, a small time crook could start a "software engineering consulting firm", where he is the sole proprietor. Then, other criminals with their own businesses could hire his firm to consult on software and pay him thousands of dollars, when in fact no actual work is done. On paper, however, one cannot tell the difference. It is easiest to launder money when the person is paid in cash, which cannot be traced to the purchaser. If checks or bank accounts are used, the money can easily be traced to an accomplice, implicating them in any criminal charges.
In a more complex case, the money is typically sent through a huge network of overseas transactions. When it finally arrives back into the person's account, it will take a long time to retrace the steps and determine what was going on. In some cases, a corrupt banking official will assist in covering the tracks.
Banks are often used for laundering since the payee can simply open an account and deposit the money into the bank. The bank is either owned by the individual receiving the money or a criminal organization. Casinos are also very good for money laundering since the payees can simply lose their money to the casino. The person getting paid could be employed by the casino or "win" the money.
Money laundering became largely popular in the 20th century with the rise of organized crime during prohibition. The large criminal organization La Cosa Nostra used the process on millions and millions of dollars, although the government eventually passed laws that allowed prosecution of such businesses to happen more easily. Today, money laundering is still used to hold back the federal agencies, most often in illegal drug enterprises.