A poorly executed secret tryst - that isn't a secret to anyone.
It is a reference to the disappearance of South Carolina Governor Mark Sanford who "disappeared" for a week to Argentine on a romantic escapade. His staff and office told the news media that he was "hiking the Appalachian trail."
I'm sorry, Carol, I can't go to your mother-in-law's Tupperware party this evening. I'm hiking the Appalachian Trail with that new secretary from the office... in Argentina.