Pickman is a man with a strong dislike for raiders, killing anyone that wanders into his home. While generally presenting himself as collected and polite, he's extremely disturbed; casually mentioning his hobby of collecting the raiders' heads.
The Sole Survivor first meets Pickman deep within the tunnels of Pickman Gallery while he is being attacked by Slab, a raider who wants to take revenge on Pickman for killing his men.
If the Sole Survivor kills Slab and the two raiders on either side of Pickman and then speaks to him after, they are rewarded with Pickman's key, which opens a safe on the ground floor of the Gallery, containing Pickman's Blade and Pickman's thank you note. If the Sole Survivor opts to kill him, or let the raiders kill him, his corpse can still be looted, but the note will not be in the safe.
It's possible to first learn of Pickman by looting a murdered raider previously killed near Pickman gallery, as well as a random encounter of bodies placed elsewhere in the Commonwealth. His calling card is in the form of a note and left in the raider's inventory. Reading it shows him taunting other raiders and attempting to make them come to Pickman Gallery and depicts an image of a heart drawn in blood, presumably of said raiders. If the player character hasn't discovered Pickman Gallery yet, opening the note will mark its location on the map and give them a misc objective to investigate the location.
The following is based on unverified behind the scenes information and has not been confirmed by canon sources.
Pickman is named after and based on the uncanny artist Richard Upton Pickman from the short story Pickman's Model by H. P. Lovecraft.
This character also makes an appearance in Lovecraft's story "The Dream-Quest of Unknown Kadath," and this Pickman is described as having become a ghoul (though the description has little in common with the Fallout variety).
End of information based on unverified behind the scenes information.