basically the "face" of the board.
the guy who will talk to the media.
links the manager and players to the owners.
Operational Boss. It´s, as the name suggests, someone that executes something...
(S)He´s the (wo)man in charge of upholding (tactical/operational deployment and use of corp resources) the board directives (business strategy).
It's the executives' top position and only seldom outranked (as corporate organics go) by some board NON-executive officers, whose main function is to oversee the corporation itself rather than managing it
http://en.wikipedia.org/wiki/Chief_executive_officer
Perhaps that will explain it a little to you. Don't forget that top football clubs are multi-million enterprises.