Origin
The Black Stones were special stone that the Mi-go wrote their logs on, once they arrived on Earth,being sent as advance scouts by the Old Ones.
The Mi-go set up outposts in remote areas such as Antarctica, Greenland, the hills of Vermont, the Himalayas, the Australian Outback and many other such remote areas. When the invasion of Earth, planned by the Old Ones, was thwarted by the forces of Good and Evil, the Mi-go went into suspended animation.
However, they kept their Black Stones with them and guarded them from intruding humans over the centuries.
Henry Akeley and Albert Wilmarth
In the 1920's, a man living in the hills of Vermont, Henry Akeley, discovered the Black Stone of the Mi-go's Vermont outpost. He contacted a Professor Albert Wilmarth of Miskatonic University, and informed Wilmarth about the stone. However, before Wilmarth had a chance to examine it, Akeley mysteriously disappeared without a trace, supposedly captured or killed by the Mi-go. The Black Stone he found disappeared with him.
The second Black Stone found in Vermont
In 2014, Rex Buckland and Hannah Webster were invited to Vermont by Bill Kline a colleague of Rex’s at Stanford. Kline had found a second Black Stone and wanted Rex to translate the writing for him. Rex discovered the connection to the Old Ones, via translating some of the writing on the Black Stone, and tried to warn Kline about it. However, Kline mistook Rex’s concerns for professional jealousy. Kline believed Rex wanted to claim the Black Stone for himself, and refused to cooperate with Rex and Hannah any longer.
That night, Kline was attacked by the Mi-go, who had awakened to protect their Black Stone, and he went insane at the sight of them.
Over the next several days, Rex and Hannah, with the help of Randolph Carter, (this was their first encounter with him) pieced together the story of the Mi-go. Using his copy of the Necronomicon, Rex opened a portal to Yuggoth, in which the Vermont Mi-go used to return to the dark planet.
As for the second Vermont Black Stone that Kline found, it is now at Miskatonic University, where it is being further studied.
Hastur's black stone
Another Black Stone, that told the account of the Old One called Hastur, was kept by the Mi-go in their Himalayan habitat.
On June 20th, 1887, British troops, on an expedition to the Himalayas, found the stone and brought it back to Fort Albert, located in the nearby British Raj.
Rex and Hannah, having learned of these events, travelled back in time to 1887 to examine the stone. They soon confirmed that the stone was Mi-go in origin. Rex and Hannah then tried to convince the commander of Fort Albert, Colonel Robert Westphalen that the Mi-go would attack the fort to recover the stone. However, Westphalen didn't believe them.
That night, the Mi-go attacked the fort and the British casualties mounted. Rex and Hannah told Westphalen to pull his men back, that they could not fight the Mi-go. Westphalen soon agreed, but not before twenty-seven of this men were rendered permanently insane by the Mi-go. The Mi-go then recovered their stone and departed the fort.
Upon their return to 2017, Rex and Hannah transcribed the writings from the stone and learned of Hastur for the first time.
References
The Whisperer In Darkness by H.P. Lovecraft
Rex and Hannah Chronicles Story No. 32: The Black Stone
Rex and Hannah Chronicles Story No. 45: The Siege Of Fort Albert
Rex and Hannah Chronicles Story No. 46: The Island