To understand what an interlocking directorate is, one must first understand something about the management of major corporations. Major corporations operate under the control of steep managerial hierarchies, with ultimate power vested, in principle, in the board of directors. (In actuality, corporate governance has become corrupted, with CEOs typically appointing the boards instead of the reverse.) Boards are comprised of anywhere from 10 to 25 members. They meet one or two days at a time some ten times a year. Between meetings they review reports and various forms of business intelligence. Board committees will also meet with top management. A smaller, executive committee of the board will typically meet more frequently.
Boards hire and fire the highest level managers, control all significant policy changes, and steer the corporation through any crises that may arise, including such things as mergers. They also speak on behalf of the corporation to other corporations, and, on occasion, to the public as well.
CEOs will often serve on the boards of other corporations, in part as a matter of prestige, as this illustrates that their advice is valued outside of their home corporation, but also as a means of obtaining valuable, and perhaps sensitive and privileged, business intelligence, and as a means of extending their own social networks. Outside directors of this kind, usually members of the upper class, sometimes own substantial shares of the companies on whose boards they serve. Their social backgrounds, together with their vested interest in corporate wealth and power often result in a highly conservative and elitist outlook.
Highly interlocked corporations, such as David Rockefeller's Chase Manhattan Bank, are well positioned to exercise a certain measure of influence over the corporate community, and to informally enforce some degree of ideological discipline. (For a list of the most interlocked corporations, follow this link.)
Because of the strong potential for collusion and the emergence of anti-competitive practices, and the increased political leverage that can result from interlocked directorates, they were made illegal in the US early in the 20th century among competing businesses (see this link on the Clayton act and the Sherman antitrust bill). Unfortunately, especially in the case of the media, they aren't currently illegal among non-competing corporations. There's nothing, for example, to prevent a major corporate advertiser from sitting on the board of a media company it advertises with.
Interlocking directorates are only one means by which corporations exercise political and economic influence. Also crucially important are "campaign contributions" (which arguably amount to a system of legalized bribery), and the many corporate trade associations and politically influential organizations such as the National Association of Manufacturers, The Chamber of Commerce of the United States, and, above all, the Business Roundtable. As documented in the Media Essay linked below, media ties are also extensive.
To better understand the way corporate influence is exercised and its significance for everyday life see:
Who Rules America?, by G. William Domhoff
When Corporations Rule the World, by David C. Korten
Cutting Corporate Welfare, by Ralph Nader