Chairman, or sometimes, chair or conchair, is the title generally bestowed upon the person who heads the concom for a science fiction convention. (Another title occasionally used is Convenor.) Traditionally, anything that the convention does is the chair's fault, as responsibility flows upwards. However, a couple of early Australian natcons had separate positions for Organiser and Chairman.
At large conventions, which are typically organized hierarchically, there are also department chairs.
Co-chairmen (or even Tri-chairmen) are frequently tried -- usually on the theory that two people, neither of whom could do the job on their own, can somehow handle the added complexity of coordination with their co-chair -- but this usually end badly. It's hard enough for one person to keep their mind straight!
Some fen think that they will get lots of egoboo by being a conchair, but usually only otherwise flamboyant individuals get much attention in that role, even at Worldcons, and even then it's because of some sort of controversy. For example, "Dave Kyle Says You Can't Sit Here!" indelibly branded on the minds of fans Kyle's chairmanship of Nycon III in 1956, and the controversial decisions made by the concom for Big Mac in 1976 caused Ken Keller to be enshrined in fannish memory (complete with a filksong lampooning "Dear Kindly Chairman Keller"), but who remembers anybody since then without looking it up on the ?
Basically, it's a job where you can seek glory or a good convention, but not both.