Now his father has it in Salem—you know Pickman comes of old Salem stock, and had a witch ancestor hanged in 1692.
The Salem Witch Trials form a part of the New England backdrop for the stories of H. P. Lovecraft, with several ties both direct and obscure to the incidents that happened in Salem Village. Lovecraft himself visited Salem and Danvers during his lifetime, and the atmosphere of those places went into his descriptions of "witch-haunted Arkham." One such visit he recounted at some length, which I won't repeat here due to length.
The single most influential work on the Salem Witch Trials which Lovecraft ever read, and which influenced his later writing, was The Witch Cult in Western Europe (1921) by Margaret Murray, which Lovecraft read in 1923.
Murray takes it as a given that the Salem Witches were an American coven in the context of her "Witch-cult Hypothesis"; although she does not go into full detail on the trial and its aftermath, she makes several references to this throughout her book, for example:
The organization of the hierarchy was the same throughout Western Europe, with the slight local differences which always occur in any organization. The same organization, when carried to America, caused Cotton Mather to say, 'The witches are organized like Congregational Churches.' This gives the clue at once. In each Congregational Church there is a body of elders who manage the affairs of the Church, and the minister who conducts the religious services and is the chief person in religious matters; and there may also be a specially appointed person to conduct the services in the minister's absence; each Church is an independent entity and not necessarily connected with any other. In the same way there was among the witches a body of elders—the Coven—which managed the local affairs of the cult, and a man who, like the minister, held the chief place, though as God that place was infinitely higher in the eyes of the congregation than any held by a mere human being. In some of the larger congregations there was a person, inferior to the Chief, who took charge in the Chief's absence. In Southern France, however, there seems to have been a Grand Master who was supreme over several districts.
Lovecraft took this as bonafide fact, and incorporated it into both his general idea of history and his fictional milieu. For example, in the (non-fiction) essay "Supernatural Horror in Literature," Lovecraft would write:
Much of the power of Western horror-lore was undoubtedly due to the hidden but often suspected presence of a hideous cult of nocturnal worshippers whose strange customs—descended from pre-Aryan and pre-agricultural times when a squat race of Mongoloids roved over Europe with their flocks and herds—were rooted in the most revolting fertility-rites of immemorial antiquity. This secret religion, stealthily handed down amongst peasants for thousands of years despite the outward reign of the Druidic, Graeco-Roman, and Christian faiths in the regions involved, was marked by wild “Witches’ Sabbaths” in lonely woods and atop distant hills on Walpurgis-Night and Hallowe’en, the traditional breeding-seasons of the goats and sheep and cattle; and became the source of vast riches of sorcery-legend, besides provoking extensive witchcraft- prosecutions of which the Salem affair forms the chief American example.
The extent to which Lovecraft appears to genuinely believe that there was an underground religion organized along the lines that Murray suggests can be seen in the numerous references in his letters, where he combines Murray's hypothesis with euhemeristic ideas of an precursor race in Europe, as presented in fiction by Arthur Machen. In Lovecraft's synthesis of Machen and Murray, the witch-cult in Salem came from Europe, and the European witch-cult had inherited a pagan religion that predated the coming of Caucasians to Europe. If you want to read more about that, you can read Conan and the Little People: Robert E. Howard and Lovecraft's Theory.
Once, Lovecraft explained the whole of the affair (as he understood it) to his friend:
To me, this background seems to explain all the New England witch trials (the first was in 1648) up to the time of the Salem scare. The witch-cult was not here, but its echoes and traditions were. Trials were by no means numerous, and executions very few. Then came Salem with its 50 trials and 19 executions, and with the strange parallelism of testimony in many cases, which profoundly impressed some of the most scholarly men in the Province. Cotton Mather—a learned man who was no fool for all his extravagant Puritanism—heard and sifted the evidence, and egged on the prosecutions with all his power and influence, believing some new and definite Satanic attack to have been made upon Massachusetts. What is behind all this? Merely a natural outburst and culmination of the mood which produced the early sporadic trials—or something new and systematic and tangible?
Well, we shall never know. Miss Murray, the anthropologist, believes that the witch-cult actually established a “coven” (its only one in the New World) in the Salem region about 1690, and that it included a large number of neurotic and degenerate whites, together with Indians, negroes, and West-Indian slaves. Of this coven, she maintains, the Rev. George Burroughs was probably the leader or “Black Man”; (detailed legend, testimony, and anecdote certainly prove him by no means saintly!) so that this hanging was perfectly well merited. Of the other victims, some were probably guilty of cult participation whilst others were innocent and accused only through malice. Thus conjectures the learned author of “The Witch Cult in Western Europe”—though of course without definite proof. Others Americans who have possibly examined the Salem records more closely than she—think it improbable that any formally organised cult branch could have been concerned; though all agree that the answers to trial questions shew a vast familiarity with cult institutions—more than could easily be accounted for by common legend, or by any sort of leading questions. For my part—I doubt if a compact coven existed, but certainly think that people had come to Salem who had a direct personal knowledge of the cult, and who were perhaps initiated members of it. I think that some of the rites and formulae of the cult must have been talked about secretly among certain elements, and perhaps furtively practiced by the few degenerates involved. I would not be surprised if Burroughs were concerned—and also the West Indian slave woman Tituba, who started the scare in the first place by telling tales to neurotic children. Most of the people hanged were probably innocent, yet I do think there was a concrete, sordid background not present in any other New England witchcraft case. Puritan witch-belief by no means ended with Salem, although there were no more executions.
The fictional use of the witches of Salem (and their supposed descendants) was nothing new in pulp fiction; Herbert Gorman had done it in "The Place Called Dagon" (1927), among many others - but Lovecraft's influence would be felt in increasing the popularity of the idea. Robert Bloch (with Lovecraft's assistance) would write about a group of witches descended from Salem in "Satan's Servants" (1949); Lovecraft's "The Dreams in the Witch House" (1933) (set in Arkham) would inspire Henry Kuttner's "The Salem Horror" (1937).
In the late 1920s/early 1930s, Lovecraft's publications in Weird Tales attracted the attentions of a few odd occultists, one of whom claimed:
By the way—that tale has just earned me a highly interesting letter from a curious old lady in Boston, a direct lineal descendant of the Salem witch Mary Easty, who was hanged on Gallows Hill Aug. 19, 1692. She hints at strange gifts & traditions handed down in her family, & asks me if I have access to any ancient secret witch-lore of New England. Also, she wants to know if Dunwich & Arkham are real places! I shall answer the letter, & see if I can get the good old soul to relate some of the whispered witch-traditions! A story of Salem horror based on actual “inside dope” from a witch-blooded crone would surely be a striking novelty!
Lovecraft never goes into great detail regarding this person, so we don't know their actual identity or how long the correspondence went on, but it gives a taste of Lovecraft's understanding and approach to the whole affair.