An Agile Coach is not just about coaching (part 1)

"Agile Coach" is an extremely overused term today: it seems like every company wants one and lots of people refer to themselves as that. But what does it actually mean? An external consultant? The iteration manager (aka Scrum Master)? The person who facilitates collaborative workshops? An agile project manager? A trainer talking about agile? Someone who visits once a week and advises the team?