Expiators are player-assembled machines found in a hell biome. An expiator is similar to a purifier in that each expiator is made of seven different parts that are scattered throughout the world in industrial chests found in bunkers and dungeons. An expiator allows you to deliver ghosts, which is necessary for removing the 12 deadly purple infernal protectors in each hell world. In addition, releasing ghosts will enable you to get XP and the deliverer achievements. Even the simple act of discovering parts to an expiator has benefits: it gives relatively large XP rewards and contributes towards the infernal scout achievement.
How to Obtain
You can't obtain an expiator into your inventory. You can, however, create a cool build that will enable people to more easily bring ghosts to it.
How to Use
Once activated, the expiator is the means by which players can deliver the lost souls of friendly ghosts. Note that friendly ghosts are the little white ones that look like semi-transparent players and walk around on the ground, not the scary grey ones (revenants) that float around moaning and blowing lethal smoke at you.
To activate an expiator, first find all 7 parts in industrial chests around the world. Then go to the expiator itself and click or tap it once to activate it (which counts as finding the 8th part). You can see how many parts have already been found by looking at the sidebar on the minimap. Expiators, like all world machines, nearly always generate at or above a depth of -200.
Once the expiator is up and running, all you have to do to deliver a ghost is tap or click on the expiator when a friendly ghost is nearby. The ghost must be within 5 blocks of the expiator's anchor block (the bottom left block of the machine). Each ghost you deliver will give you between 25 and 30 XP, depending on your Order of the Moon status. Note that at this time (February 2016), if you have more than one ghost within range, tapping/clicking the expiator will release all of them at once, but will only give you XP for one instance of delivering.
In addition, each delivered soul will randomly cause one of the twelve deadly infernal protectors (often called IPs) in the world to disappear, allowing players to loot the large red chest it had been protecting.
One way to get ghosts is to mine a bloodstone tombstone. But be aware that revenants will often spawn this way, too!
An easy way to get ghosts is to go up to the surface just above the expiator and bury skeletons like you would do for the undertaker achievements. Eventually this process will spawn a friendly ghost, which you can then lead down to the expiator.
When an infernal protector disappears, the purple glow also disappears, so it's helpful to mark the purple areas BEFORE you begin using the expiator to deliver ghosts.
You can mark the purple areas with plaques or even landmark plaques, or use an item that displays an icon on your minimap, like a micro protector, spawner, or stabilizer. If you have enough teleporters, simply placing one at each infernal protector, and then another at the expiator itself, will make it a snap to jump to the dungeons after each released ghost to quickly find which infernal protector has been destroyed. Or you can simply make note of the coordinates ahead of time and write them down.
On public hell worlds, players will sometimes put protectors over the expiator before all the parts have been found or all the infernal protectors have been removed. Sometimes they'll do this in order to keep the expiator available to all. Other times, they'll do it to temporarily render the expiator unusable so that people won't accidentally or otherwise release ghosts before all the infernal protectors have been found and marked. And some players do it just because they want to keep all the infernally protected dungeons for themselves. So if you find a hell world where there are still some parts missing, or where you can see there are still purple infernal protectors around, it's a good idea to search for the expiator before spending a lot of time marking dungeons and such, to see if it's been blocked off or not. Since many players who block expiators will also build an enclosed tunnel stretching up to the surface, one way to quickly scan for a protected expiator is to skim along the surface of the world looking for such a structure.