Without even reading that link you provided, "OMAHA" is an audible. It is used to change a play in the line of scrimmage. Example.....when I say OMAHA that may mean that I want my wideouts running a certain pattern. If I see some funny stuff going on with their lining up on defense, I may change my audible to mean running the ball to the left part of the line for instance. Omaha can mean a certain play for a certain number of times, and changed on the spot or line of scrimmage to mean something else. Those that need explaining what "OMAHA" means as Payton yells it out probably never played football before nor understand the game because they never played football before. If I sense a blitz coming, I can throw in an audible like the color "SILVER" so that my linemen and running backs are aware that a blitz is coming, and therefore the wideouts know the quarterback is going to dump it fast to them so they should probably keep a short but sweet route to burn the blitzers. It's a way of communicating to your team to act upon an impending defensive action.