So in chronological order, it would appear that some of the key concepts are:
- The Great Ones: A race of elder gods or "old cosmic horrors" in the vein of Lovecraft's Cthulhu Mythos. They propagate their kind by selecting humans as surrogate mothers, producing lesser monsters and, on rare occasions, new Great Ones. They exist in an alternate dimension, overlapping the human dimension, but hidden from human sight by Rom the Vacuous Spider, who may or may not have been a student at Bygernwerth, but is now something similar to a Great One, maintaining the veil.
- Pthumerians: A first race of men, like the Hyperboreans in other fiction, predating the modern-day city of Yharnam by eons.
- Queen Yharnham, ruler of the ancient Pthumerians, who the Great Ones chose as the surrogate mother for a new Great One. Perhaps the Great One she birthed is the one simply called Moon Presence, which takes the form of the red moon. It appears she became something akin to a vampire or undead, and is the source of the blood that the Healing Church uses to cure the ill and mend the wounded. She is also likely the "holy medium" the church found in the tombs of the elder gods deep beneath the city, and who allowed the church's ruling class, the Choir, to establish contact with the Great Ones.
- Moon Presence: Speculation on my part, but as I said earlier, the Moon Presence might be trying to reproduce itself. It may have brought about the dream-like state Yharnham now finds itself in, including the Plague of Beasts, and the Hunt it necessitates, which would lead to the discovery of a warrior strong enough to serve as a surrogate for the infant Great One. This would explain how it appears to hold dominion over the Hunter's Dream. Of course, by killing Moon Presence, you actually become the infant Great One.
- The Healing Church: Practitioners of the healing ministration of blood transfusions, using blessed blood (presumably from Queen Yharnam, discovered beneath the city). They have also established contact with the Great Ones. The Celestial Emissary would appear to be a diplomat sent by the Great Ones as a liaison with the Healing Church, hence its presence in the church garden. Ebrietas, Daughter of the Cosmos, would appear to be another "visiting dignitary," so to speak, and once Rom is killed, she sets about trying to revive him at her Altar of Despair in the Upper Cathedral.
- Byrgenwerth: An academy set up in the countryside to study findings from the tombs of the elder gods (the Chalice Dungeons, deep beneath Yharnam). They go mad with occult knowledge and start transforming into monsters. Possibly "ground zero" for the Plague of Beasts (speculation on my part). The game states the Healing Church ordered Byrgenwerth closed and sealed off the surrounding forest, hence the name, "Forbidden Woods." Home now only to cultists such as the snake-men, only church officials who know the password can enter this forsaken place. This why you seek out Vicar Amelia in the Grand Cathedral -- you learn the password at her altar.
- Mensis: A school that split off from Byrgenwerth, presumably upon its closure, to continue establishing contact with the Great Ones. They wear cage-like headwear that keeps the Great Ones from outright shattering their mental faculties. They are still mad, however, and seek to birth the new Great One. It would appear that the abomination called "the One Reborn," descended from the red moon of Moon Presence, is perhaps a botched attempt at this. It would also appear they are abducting sacrificial subjects from Yharnham, whisking them off to their Unseen Village, perhaps to serve as potential surrogates for the infant Great One they are attempting to birth.
This hardly covers everything, but these are some of the concepts as I understand them. Feel free to correct.