The arrow points from the country you guessed toward the secret country, as one of eight compass directions: N, NE, E, SE, S, SW, W or NW.
The direction is the initial heading of the shortest route over the Earth. Over long distances that route curves, so a guess far away can point somewhere that looks surprising on a flat map.
The “Closer” and “Farther” labels compare each guess with your previous one.
See also How distance is measured. For tips, read the Closer or Farther tips and strategy.