For a man to have vaginal sex with a woman who is not his wife. Can be used as a reference to a married man having an illicit sexual affair, and deceiving everyone about it by telling them he's doing something else.
"The Appalachian Trail" refers to the woman's vagina.
Mark Sanford, the Governor of South Carolina, flew to South America to see his mistress and told everyone, including his staff, that he 'would be gone for a few days hiking the Appalachian Trail.'
"Does Bob's wife know he's taking that hot secretary with him on his business trip? Looks to me like he's planning on hiking the Appalachian Trail."