First, the basics of Expedition
To put it shortly, an Expedition encounter is a much more interesting form of archaeology, with monsters involved. All jokes aside, Expedition encounters can be done in Atlas nodes with a White icon and a six-pronged star. In Waystones with such nodes, you can meet one of the four Expedition NPCs who will overlook a field of excavation markers and Path of exile currency explosives.
Once you encounter this setup, you'll be given a couple of explosives you can plant around the excavation site. Once planted, they'll blow up the site in the sequence they were placed. The bombs will dig up any buried chest and enemies underground, after which the latter will start attacking you.
These enemies will drop currencies upon death, tied to the NPC that overlooked the excavation site. Furthermore, the sites can play host to POE currency for sale remnants that can imbue enemies with their specific effects. Additionally, these remnants can stack up and be applied to any enemy spawned after the remnant is destroyed.
The NPCs that can be encountered and their associated currencies are as follows:
Black Scythe Artifact - Tujen
Broken Circle Artifact - Gwennen
Order Artifact - Rog
Sun Artifact - Dannig
Exotic Coinage is the fifth currency that is considered universal.
The Wall