When digging or mining there is a chance you will find a treasure map.
How to find the treasure:
Use your compass (inventory item) with the map to get directions. You do this by activating one item (compass or map; double-click and it turns green in inventory/activated) and then right clicking on the other item.
Narrow down the tile the treasure is on by repeatedly using your compass with the map as you get closer. Note that the direction it gives you is based on the direction you're facing.
Once you find the tile use your shovel on the map to dig up the treasure.