What are the mechanics for establishing professorial chair in a university?
A chair can be either the head of the department (as described by another answerer) or it can be an endowed chair position. A chairperson in the first sense is the head of the department, and is responsible for all of the administrative responsibilities in running that department. A chair in the second sense is a professor who is hired to fill a position in a specific area of study. Their salary is fully or partially paid by an endowment given to the university by a donor who wants to make sure that a certain subject is taught (and researched) in that university. It takes millions of dollars to endow a chair, and the chairship is usually named after the donor. For example, a professor could be the Claire Booth Luce Chair for Women in Science. That means that Claire Booth Luce donated a lot of money to the university in order to make sure that university would always have a professor who taught courses about issues of women in science. That professor might also be required to run a program that encourages women students to pursue study in the sciences. I hope this helps!
It's just a fancy term used in some universities for a tenured professor who is also head of his falculty. Say their are 5 tenured math profs, the chair or chairman of the faculty is the senior member in their meetings. If you belong to a club their is usually a chair which is a word used tmeaning chairman or chairwoman.