"A corporation, whether for-profit or nonprofit, is required to have a governing Board of Directors. To explain, a corporation can operate as a separate legal entity, much like a person in that it can own bank accounts, enter into contracts, etc. However, the laws governing corporations require that a corporation ultimately is accountable to its owners (stockholders in the case of for-profits and the public with nonprofits). That accountability is accomplished by requiring that each corporation has a Board of Directors that represents the stockholders or the public...
Governing Boards can have a variety of models (configurations and ways of working), for example, "working Boards" (hands-on, or administrative, where Board members might be fixing the fax one day and strategic planning the next), "collective" (where Board members and others in the organization usually do the same types of work -- it's often difficult to discern who the Board members actually are), "policy" (where Board members attend mostly to top-level policies), "Policy Governance" (trademark of Carver Governance Design, where there are very clear lines and areas of focus between Board and the CEO), etc. All of these models are types of governing Boards.
Boards can have a broad range of "personalities." For example, Boards of large for-profit and nonprofit corporations might be very formal in nature with strong attention to Parliamentary procedures, highly proceduralized Board operations, etc. In contrast, Boards of small nonprofit or for-profit corporations might be very informal in nature. Some people believe in life stages of Boards, including that they 1) start out as "working" Boards where members focus on day-to-day matters in addition to strategic matters, 2) evolve to "policy" Boards where members focus mostly on strategic matters, and 3) eventually become large, institutionalized Boards that often have small executive committees and maybe many members some of which are "big names" to gain credibility with funders or investors..."
The above gives a basic overview sketch of the role of a governing Board. The Free Complete Toolkit for Boards from Carter McNamara provides more information about the roles and responsibilities of Boards and Board members, including job descriptions for each of the common positions on a Board and much, much more.