A country mile is much longer.
A mile is the distance at some time run by, say, Steve Cram or Seb Coe, in the olden days. It is 1.6 km, or 1,600 metres, or 1,760 yards.
Whereas ...
If you were to stop outside a village pub in, say, Gloucestershire or Somerset, and ask the distance to your destination of Little Buttcrack, or Lower Piddlington, they would tell you ...
... "arr, that be about a mile, that be".
In fact, as it will transpire, your destination is probably still about twelve miles away.
Hence ... "country mile".