The RouteOptions parameter Precision sets the minimum distance between points on a route; that is, the shape generalization of the route. The larger the value, the fewer points are used to draw the route, and the faster the response time. Precision units are decimal degrees; there is no upper limit. If a map is requested from the Map Image Web Service, precision is ignored and the route is generalized to the resolution of the map.
You could, for example, set precision to the pixel size in decimal degrees of your map. That would give you a route that had a maximum of one point per pixel and a relatively fast drawing time. The default value for precision is '0', which means no generalization. It is not used when a map image is included with the route.
There is no easy conversion from angular units such as degrees to linear units such as meters or miles, though there is some useful information in the ArcGIS Desktop Help.