A Chairman of the Board runs the board of directors for a corporation. He hires the CEO and along with the rest of the board, makes sure the company is in good financial shape and is doing its best to fulfill its mission statement. He is like the General Manager of a sports team, who hires the coach and makes sure the team business is being run efficiently. It goes without saying, of course, that the Chairman can be a woman (in which case she’d likely be referred to as the Chairwoman, Chair, or Chairperson of the Board).