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