These can arise when somebody (the principal) hires somebody else (the agent) to carry out a task and the interests of the agent conflict with the interests of the principal. An example of such principal-agent problems comes from the relationship between the shareholders who own a public company and the managers who run it.
The owners would like managers to run the firm in ways that maximise the value of their shares, whereas the managers' priority may be, say, to build a business empire through rapid expansion and mergers and acquisitions, which may not increase their firm's share price.
One way to reduce agency costs is for the principal to monitor what the agent does to make sure it is what he has been hired to do. But this can be costly, too. It may be impossible to define the agent's job in a way that can be monitored effectively. For instance, it is hard to know whether a manager who has expanded a firm through an acquisition that reduced its share price was pursuing his own empire-building interests or, say, was trying to maximise shareholder value but was unlucky.
Another way to lower agency costs, especially when monitoring is too expensive or too difficult, is to make the interests of the agent more like those of the principal. For instance, an increasingly common solution to the agency costs arising from the separation of ownership and management of public companies is to pay managers partly with shares and share options in the company. This gives the managers a powerful incentive to act in the interests of the owners by maximising shareholder value. But even this is not a perfect solution.
Some managers with lots of share options have engaged in accounting fraud in order to increase the value of those options long enough for them to cash some of them in, but to the detriment of their firm and its other shareholders. See, for example, Enron.