Hero's Path Mode is given by Robbie after completing the quest "Presenting: Hero's Path Mode". Note that the Hateno Village Research Lab must be completed before the required quest can be triggered.
How To Use Hero's Path Mode
The Trail For The Past 256 Hours Is Shown
Open the map and press the X Button to use the Hero's Path Mode. Using this will allow you to see where you have traveled for the past 256 hours and the places you have never been before. After 256 hours, the oldest paths are deleted from the list.
You Can Also Look Back At the Playback
While in Hero's Path Mode, press the X Button again to playback. This will trace back through the saved trails from the oldest to the newest. It will also show you where you died, so you can use it to look back on your gameplay.