In the late 1700's, many houses consisted of a large room with only one chair. Commonly, a long wide board folded down from the wall, and was used for dining. The "head of the household." always sat in the chair while everyone else ate sitting on the floor.
Occasionally a quest, who was usually a man, would be invited to sit in the chair during a meal.
To sit in the chair meant you were important and in charge.
They called the one sitting in the chair the "chair man:.
Today in business, we use the expression or title
"Chairman" or "Chairman of the Board."