Ok, when you get to the area marked on your map for this mission, you need to:
1. Clear the area of people (in this case vagabonds).
2. Go to the area that is marked on the map and look for a rough pile of stones on the ground.
3. Select the special stone you were given (in your inventory) while standing on the rough pile of stones.
Once this is complete, a flaming Pentagram should appear on the ground underneath you, and you should have lost half your HP.
If this has happened, you have successfully completed the quest.
Now you may turn it in or continue to do other quests.