Out of that simple non-legal definition has grown a vast service industry covering commercial and many other risks and providing consulting and financial services. Directors' and officers' liability insurance falls into the latter class. The policy may or may not protect the company as well as the individuals. Because some companies have the power in their charter, they may agree to indemnify and hold harmless directors and officers from claims. To protect itself, the company might acquire a separate type of insurance policy called a Company Reimbursement Policy.
Practices obviously vary.
For instance, few policies will cover fraud, dishonesty, fines, penalties, deliberate criminal acts, etc. This was essentially because Americans are the most litigious of any nationality on the planet. They love to sue to protect their rights and recover damages for their breach. Those awards can sometimes be very high. Many other common law countries, i.e. those with a British heritage, such as the U.K., Canada, Australia and New Zealand, soon followed the U.S. practices.