Here is a good legal definition of fiduciary duty from Cornell Law website.
A fiduciary duty is a legal duty to act solely in another party’s interests. Parties owing this duty are called fiduciaries. The individuals to whom they owe a duty are called principals. Fiduciaries may not profit from their relationship with their principals unless they have the principals’ express informed consent. They also have a duty to avoid any conflicts of interest between themselves and their principals or between their principals and the fiduciaries’ other clients. A fiduciary duty is the strictest duty of care recognized by the US legal system.
Examples of fiduciary relationships include those between a lawyer and her client, a guardian and her ward, and a director and her shareholders.