The Mysterious Coordinates are an item which will be dropped by any Boss until they are given to the Traveller. Giving them to him will unlock the ability for the player to Travel to the Cathedral of the Moon. Using the item wil display a message from The Medium.
ATTENTION WHOEVER FOUND THIS Please come to these coordinates ASAP. There is no time to lose. I will explain more when we meet in person. Find a boat or an equivalent and travel to the island depicted in this this drawing. Apologies if this is a bit rude. Time is of the essence here, we have much to discuss.
The coordinates in the tooltip do not correlate to any locations in the players world, they relate to a point in the perspective of Terraria as a greater continent and therefore the spot in the ocean where the island is.