A video by VaatiVidya breaks down the story of Bloodborne and explains everything that's going on... well, most of everything that he can within the confines of half an hour. If you were ever interested in the whys and hows of Bloodborne, the video does a great job of explaining it. It should go without saying that spoilers are ahead.
The video covers a lot of ground in regards to the lore of Bloodborne, and if you didn't think that there was a lot of story behind the game then you thought wrong. There's almost an entire novel's worth of content in From Software's action-RPG and it delves very heavily into Lovecraftian mythology.
Things start off with the old Chalice Dungeons... they were dug out by the Pthumerians, a superhuman race that managed to wield the power of the eldritch Truth. They could tap into the power of the Great Ones or the Old Ones.
In Bloodborne's lore, both Master Willem and Lawrence from Byrgenwerth were dedicated on learning more about the Great Ones and seeking to gain the enlightenment that they had attained. Both went about things in a different way, with Willem seeking enlightenment by attaining parts of the Old Ones and trying to replicate them, such as adding a bunch of eyeballs to people or attempting to use the umbilical cord to attain higher insight.
Lawrence, however, focused on seeking enlightenment through the Old Blood. This deviated from another method of attaining enlightenment, which was through runes that Runesmith Caryll had crafted from the language of the Old Ones. However, Lawrence was fascinated with the Old Blood and pursued making the Healing Church to administer vials of blood for healing, which is partly where the player-character comes into play.
While the Healing Church's original purpose was to heal, things became distorted when the blood was infected the people and turning them into monsters, this was spread even more-so by the ashen blood in Old Yharnam. In fact, Old Yharnam's ashen blood infection was so bad that they just had to burn it all to the ground.
A subsection of the Healing Church called the Mensis school and headed up by Micolash was designed to take the insight of the church and elevate it to a new level by traveling deep into the nightmare realm.
The Mensis school in Bloodborne sit somewhat at the heart of the story, as they attempted at all costs to communicate with the Old Ones but did so by attempting to get into the nightmare realm. Of course, their brains became stillborn while Micolash ascended to the nightmare realm and became trapped, along with Queen Yharnam.
If players manage to get through the nightmare realm and defeat the boss they'll come to a startling realization: the Hunter's Dream was actually conceived by a Great One and that Hunter Gehrman is actually trapped there, working as a conduit to help other hunters pass through and fight against the Old Ones in other nightmare realms.
Essentially, the ending of Bloodborne lets players choose how things unfold, as they can either defeat the Great One under the Pale Moon, become a conduit and replace Gehrman or leave the Hunter's Dream altogether.
The game's lore definitely opens up some neat possibilities for future installments of Bloodborne and I'm sure the lore will be further explored in the DLC or potential sequels.