The Explorer Challenges are all about finding the hidden treasure scattered around. To complete this Challenge you'll need to find three Treasure Maps and loot the treasure at the end of the maps. The category won't unlock until you find your first Treasure Map and then it's simply the matter of following them to the end.
Explorer Challenges 1 - 10
The locations of the Treasure Maps in Red Dead Redemption 2 are covered elsewhere in this guide, take a look at the links below to find where they can be found and how to loot the treasure at the end of it.
Upon looting all three treasures, you'll reach rank 10 and unlock the Explorer Holster, Bandolier, Gun Belt and Off-Hand Holster along with 475 Stamina XP. You'll also need to complete the Explorer Challenges along with the Herbalist and Survivalist Challenges for the Dead Eye set bonus.