Definition of corporate governance
Economists have long noted that publicly traded companies suffer from an incentive problem. The people who run the company (management) are not the same as the people who own the company (shareholders) or who otherwise have a stake in its success (stakeholders).
Managers are paid professionals with their own self interests. In order to prevent managers from making decisions that benefit themselves but that are detrimental to others, a system of checks and balances is put in place. This system is called “corporate governance.” At a minimum, governance systems include a board of directors (to hire, fire, and compensate management) and an external auditor (to make sure financial statements are accurate). Other constituents such as creditors, customers, suppliers, labour unions, the media, and regulators also play a role in corporate governance by making sure that management behaves appropriately.
It is easier to point out examples of “bad” governance than “good” governance. The most famous example of bad governance is Enron. Executives lied about Enron’s financial results for years in order to increase the value of personal stock options. Their actions went undetected by the board, the auditor, ratings agencies, regulators, and the media for many years until the company ultimately collapsed into bankruptcy. If Enron had had a more effective governance system in place, this behavior would have been detected many years earlier and management would have been replaced. 
Financial Times definition
How a company is managed, in terms of the institutional systems and protocols meant to ensure accountability and sound ethics. The concept encompasses a variety of issues, including disclosure of information to shareholders and board members, remuneration of senior executives, potential conflicts of interest among managers and directors, supervisory structures, etc.