Like, on a lore basis.
Is it like, you’re ripping the life out of enemies and giving it to your allies? Are you inspiring allies to be better and then they feel better (going off the meaning of the word atonement)? Do you have extra holy magic sitting around after attacking and you use that to heal?
I don’t know if there actually is a lore representation of it, but I’m curious.
(Disciplines, discipline me if I’m wrong)
I’d imagine it’s like a soul tether with you apply atonement and then that say ‘Mind blast’ you’re hitting on an enemy is motivating and healing your ally.
It’s kinda like you’re with your friends and you roast someone/something you don’t like and it improves your friends mood.
The only way I can possibly make sense of it is that you are causing your enemies to atone, which in turn is healing your allies. I can’t really wrap my head around it any other way, but also I think it is a reach.
I think you ask for it, then you just get it.
your enemies are atoning for attacking your allies by giving them some of their life force
The way I always saw it is that their magic dmg cleaves in healing ways, instead of cleaving to hurt enemies the cleaving effect is healing allies.
Sort of like the more your enemies die the more your righteous allies gain life, but just in a much more direct way. Sort of like Tom Cruise in minority report.
If you can explain the magic is it still magic? Any sufficiently advanced magic is indistinguishable from science after all
Magic still generally has a concept, it just doesnt have to align with reality.
As confusing as any Cleave
Nah, magic can be explained while still being magic. You’re just manipulating reality through various non-physical means.
For example, fire mages create the conditions for fire by manipulating reality with order magic. There are NPCs you can follow around in Stormwind who talk about formulae, sigils, runes and how sciencey magic can be.
Druids channel life magic to make your body heal itself.
Shamans use water magic to cleanse away pain / magic / whatever and heal you.
Holy priests use the light to heal you directly, same with pallies.
Prevokers use some druidic magic, but they also turn back time on wounds to just reverse wounds. Dragon fire (the kind evokers use) is also manipulating life force.
I could imagine that a monk is quite literally punching / kicking the chi out of enemies, and then they redirect that back into their allies. Something like avenging crusader I could imagine you’re just splashing light magic around because you have so much of it.
I just don’t get how atonement works.
I could see that, and atonement is just you aiming at certain people maybe.
My only issue though is that shadow magic also heals people. Like if I Shadow Word: Death, that’s certainly not a healing spell that will cleave, but it still heals people.
Just like how Jesus gave his life to atone for the world’s sins, saving us all. Your enemies atone for their sins by saving his enemies life force.
Overall, just bs, but you get the picture.
I think it’s some sort of mark that lets allies not be hurt by your holy magic period. Kind of how a holy spell can hurt undead but heal the living (in most cases at least), applying atonement means when your holy attacks land allies in the metaphorical splash zone get healed instead of hurt. Obviously there’s no standard AoE component, but that’s how I’d look at it. Kind of like Beacon of Light in a sense.
The Priest is a real big fan of Hellraiser. It gains increased healing capabilities after causing pain.
On a more serious note, other games have something similar to Disc Priests called Castigators. They cause pain both to themselves and the enemy.
They see pain/punishment as a cleansing act.
That’s kind of how I think about it too, but then I get confused when I think about shadow magic and voidweaver. There is no healing component to most shadow magic, but you can apparently drain the life out of enemies with shadow magic a la vampiric embrace and whatnot, and I imagine you can distribute that around.
It doesn’t
They just gave it a 40 something % buff outside of raid, so it does actually work. 
Back before they went full on Void old god with Priest in BfA. Priest’s shadow magic was less of actual magic and more based on Moral concept of Dark and Light.
The Priest could be morally corrupt and evil but still heal. It is why Mind Control exists for Priest.
Now, the void stuff makes no sense at all as void doesn’t heal it consumes.
Based on the cosmology chart we saw a while back, shadow and void are distinct things, but in the same direction.
It’s like how fel is not just straight up chaos, but they’re related.
So maybe shadow has some non-consumptive properties. Anything labeled as void is all about damage (void blast, entropic rift, etc).
Though you still get healing from those, so maybe you’re consuming the energy, then just share it with people. 
Yeah, I think shadow healing via atonement is just mechanics, like how undead players aren’t immune to fear. Shadow healing in general is fine a la Shadow Mend, but that’s a different approach entirely.