The precision slider controls how many vertices are used when the route is drawn on the map. A higher precision (more vertices) will return a route that more closely matches the roads of the map, but it will take longer to draw. A route with lower precision will return more quickly, but may not follow the roads as precisely. The position of the slider does not affect the driving directions themselves; just how they are displayed on the map.
A route with a high precision cannot be generated for very long routes. If precision is too high you will receive a warning asking you to lower the precision. Usually it is not necessary to move the slider very far from the high end.