HDG, TRK, NAV Modes
HDG - Heading Mode The autopilot keeps the nose of the airplane pointed at the magnetic heading bug. If there is a crosswind, the aircraft's ground track will "drift" with the crosswind. For instance, if you wish to go to an airport that is 270 degrees from your location, but there is a wind from 180 degrees, you will end up north of your target because the crosswind pushed you north. This mode is generally only used when ATC tells you to fly a direction, since they assume you will use a compass and not a GPS to fly this vector.
TRK - Track Mode The autopilot uses GPS information to keep the ground track of the airplane on a straight line toward the heading bug. If there is a crosswind, the nose of the aircraft (heading) will not be pointed the same as the heading bug since the autopilot will adjust the heading to maintain a straight line over the ground. This is generally used any time the pilot wants to “hold” the direction of the aircraft without actually flying a specific GPS course or VOR radial. If the pilot hand flies the airplane off the track, the autopilot will correct back to the track, but this will not be the exact same line over the ground, since this is not a course line, but a ground track hold.
NAV - Navigation Mode The autopilot keeps the CDI needle that is displayed on the HSI centered. This CDI source may be a VOR, localizer, or GPS. Generally, this means the autopilot is flying you straight down a radial or direct to your GPS waypoint. This will fly you onto the GPS course or radial if you are off it when you engage the mode. If needed, the aircraft will maintain the correct heading to compensate for any crosswind. If you reach a GPS waypoint or change your desired radial, the autopilot will turn to intercept this new course.