Here's a breakdown:
* Hell: Obviously refers to the traditional concept of the underworld, a place of punishment and suffering.
* Connaught: One of the four provinces of Ireland, geographically located in the west.
The phrase likely originated from the historical perception that Connaught was a remote and less desirable place compared to other parts of Ireland.
Therefore, "to hell or Connaught" is a humorous way of saying "far away" or "somewhere undesirable."
It's a similar concept to English expressions like "to the ends of the earth" or "to the middle of nowhere."