What does: Hosted agenda counter: End the run. Mean?

It means discard an agenda counter hosted on this card to end the run.

Thanks

Just to be clear on the meaning here…so I've scored Nisei mk II and placed a counter on it. Now the runner starts a run. I can discard this counter and the run is stopped even before it begins?

David Spangler said:

Not before it begins, obviously, but at any point during a run when the corp player has the opportunity to use a paid ability (see timing chart in the rulebook or better yet the updated one in the FAQ). It makes the most sense to use it towards the end of the run, though, after the runner has fought and paid his way through your ice but before he accesses any cards.