A Board of Directors has three primary "big picture" responsibilities. The third is Senior Management – providing guidance to senior staff, evaluating the performance of senior management and determining appropriate compensation.
To function effectively, senior management and the Board must understand their distinctly different duties and roles within the organization. The Board of Directors governs the organization and senior management (along with staff) manages the organization day-to-day.
The Board generally is responsible for the selection (hiring) of senior management. They work cooperatively with and support senior staff to ensure success of the organization. They are also responsible for formally evaluating the chief executive on how well he or she is accomplishing the goals of the organization and determining appropriate compensation.
The Minnesota Council of Nonprofits has very good literature on Boards, senior management and their roles and relationships:
The Executive Director and Board Relationship
Roles and Responsibilities of the Nonprofit Board