Adella is a Nun or Blood Saint of the Healing Church. She was kidnapped by the Snatchers of Yarhar'gul, the Unseen Village and brought back there to be a part of their surreptitious rituals. Adella's outward modesty hides a jealous and unstable disposition. When met in the storeroom of Yarhar'gul during the player's first trip to the village, she'll be too scared to speak to the player unless they are wearing the attire of the Healing Church.
The Blood Saints occupy a unique position within the church hierarchy. Their very existence seems to imply that there are some humans who are not as acutely affected by the transformative powers of the blood, and are in fact, able to cultivate it within their bodies. The blood of Adeline indicates that this is a rather rare situation, as Adeline herself is regarded as one of the few cases that turned out favourably when she was treated by the Church to cultivate "worthy blood".
It may be that Bloods Saints are created to be living vessels of blood for the upper echelons of the Church, primarily used by the members of the Church to satiate their desire for blood. Both Adella and Saint Adeline seem to be very aware of their position within the Healing Church. Adella rather tellingly says to you when you refuse her offer of her "lowly blood": "Forgive me, I… I should have known better. What would a brave hunter do with lowly blood like mine? Please, forget I even asked." Adeline also makes frequent references to her "former, lesser years…" and the fact that before she became a Research Patient for the Healing Church she "used to be nothing…" so it would seem that the Blood Saints were not necessarily respected or praised within the Church.
It may be that the Blood Saints are not highly regarded because of their contact with the sick and scourge-infected. It is well known that Yharnam is the center of blood ministration, and that travellers from many lands make the pilgrimage there to obtain healing through Yharnam's famous blood. Adella's blood description says that the mere chance of being treated with the blood of a Blood Saint lends legitimacy to the Healing Church and communion - communion is the taking of blood and this description confirms that the blood of Adella and other Blood Saints holds special properties that make the effects of blood, or perhaps just the healing effects, stronger. Perhaps before the fall of the Healing Church, travellers would pay a little extra to reap the benefits of a Blood Saint's blood.
The role of the Blood Saints within the Healing Church therefore seems to be twofold; to provide a steady source of blood for the upper echelons and to provide a unique service for the sick and scourge-infected of Yharnam. Adella wears the Black Church set, a set which describes the actions of the hunters of the Healing Church. It is likely that this is simply the Healing Church's 'uniform', and that Adella does not act in any capacity as a hunter of the Church, though this could be debated.
Based on Adella's dialogue and behaviour, she seems to be very aware of different types of blood. She also seems to be judgemental, scheming and ultimately murderous. The Bigoted Old Man's dialogue can essentially be taken to mean the opposite of what is said: he will tell the player that Arianna despises the saint [meaning Adella] for having what she doesn't" whereas based on Adella's behaviour, the opposite seems to be true. Whenever the player interacts with Arianna, while Adella is in the chapel, Adella will peek around the corner to eavesdrop on what they are discussing. If the player ingests too much of Arianna's blood, Adella will eventually murder her, perhaps believing that Arianna has been misleading the player, but more likely because she is drawn to Arianna's blood, resenting Arianna for what she has.
The Blood Saints of the Healing Church are clearly conditioned to resist the urge for blood, as Adeline will say:
Don't be greedy. As they say, "Fear the thirst for blood." I should know. I was once a Blood Saint, too.
But during the Blood Moon, Adella becomes overpowered by her desires. If the player has ingested enough of Arianna's blood, then during the Blood Moon they will be attacked by Adella in the graveyard just outside Oedon Chapel. Adella tells the player that their blood is "tainted" and that she cannot help herself. This behaviour can be explained: Arianna's blood traces its roots back to Cainhurst and the corrupted blood that a Byrgenwerth scholar brought to the Queen. Where this blood came from is not explicitly stated but it seems likely that it originated from Formless Oedon, the Great One. See the Formless Oedon page for the reasoning behind this.
When Adella is killed, the Rune Oedon Writhe is found within her mind. This strongly indicates that Adella has come under the influence of Oedon while residing in the chapel and that when she says she cannot help herself, she is most probably telling the truth. It is strongly implied that the Blood Moon brings out the worst in people: "When the red moon hangs low, the line between man and beast is blurred" seems to imply that the more beast-like and selfish tendencies of humans come to the surface during the Blood Moon. This can be seen in Adella's case, and with the Older Sister character, who joyfully upholds her younger sister's ribbon despite it meaning that the younger sister has likely died. The Oedon Writhe description states "both Oedon, and his inadvertent worshipers, surreptitiously seek the precious blood", meaning the blood of the Cainhurst Queen, and if Adella is being influenced by Oedon then it is no wonder she cannot help but try to take Arianna's blood from the player's veins.
It seems likely that Adella's ideology was part of her grooming process by the Healing Church, rather than any innate character flaws but that is just speculation. Whatever the case, Adella certainly seems to have complete faith in the benevolence of the Church, shown when she states that she awaits the help of the Healing Church, despite being in such a perilous situation, even in the Church's conspicuous absence. Adella's is ultimately a rather tragic tale, despite her apparent flaws, she seems to be more of a victim than a villain.