"Mama" Murphy is an elderly seer that specializes in the "Sight," a supernatural power that she claims is sourced from chems. She takes the drugs in order to utilize her powers to predict the future. She is most likely a Psyker, as her visions do in fact come true. Hailing from Quincy, she left the town with Preston Garvey and the 20 remaining settlers when it was assaulted by mercenaries. She and the refugees were holed up in the Museum of Freedom when they were ambushed by raiders as they passed through Concord.
According to her, she was once a strong and ruthless fighter, very muscular and specialized in unarmed combat. She claims that she once ripped the head off of a raider using just her bare hands, earning her the nickname "Murphy the Madwoman."
Mama Murphy uses chems to induce a trance-like state in which she claims to see "things that were, things that will be, and even some things that are, right now." She uses her power out of a desire to protect the people she cares for, providing warnings of danger and advice on which courses of action to take.
After passing a speech check during When Freedom Calls, she will foresee a deathclaw attack. Upon completion of the quest, she may comment on how back in her youth, she killed a deathclaw with a single shot without any "fancy power armor or minigun."
Upon completing When Freedom Calls, Mama Murphy commends the Sole Survivor's success and reports the player character's son is alive somewhere in the Commonwealth.
The Sight - In exchange of drugs, Mama Murphy will use her gift to reveal some parts of the Sole Survivor's future.
After the main quest is completed, Mama Murphy can be given chems to provide insight into the ending the player chose, provided she hasn't been convinced to give up chems.
Hancock and pre-rehab Cait approve of giving Mama Murphy drugs.
Jun Long and Marcy Long will mourn the loss of Mama Murphy should she die from the Psycho dosage, with Marcy often berating the Sole Survivor and, by extension, Preston Garvey for not stopping her. Jun will seem even more depressed, bemoaning the losses everyone's felt from their journeys.
After quitting drugs, Mama Murphy will be as any other settler, and work in Sanctuary. If the player character tries to change her apparel, her standard clothes and unique turban (which is actually part of the suit) will remain hidden and unobtainable in her inventory and cannot be worn again by conventional means. Her clothes are unique to her and cannot be seen being worn by any other character in the game.
Giving Mama Murphy chems during the quest Reunions will grant the perk 'Foreknowledge' which causes Kellogg to deal 25% less damage to the player character. The perk does not have an icon and will remain even after Kellogg's death. The perk has a slight misspelling in its description, spelling Kellogg's name with only one "g."
Giving Mama Murphy chems during the quest Hunter/Hunted will give the player character the deactivation code for the Courser encountered and provides a new interaction with him.
xboxoneps4pc If one does not craft Mama Murphy's chair properly, she will be stuck sitting in the chair in the ceiling of the house in Sanctuary that has the main workbench attached. She will be above the kitchen with (usually) only her feet showing. One must shoot her feet until she falls out of the chair, then go into "edit" mode and bring the chair out of the ceiling and on the floor. She will then spawn back in normally and sit in her chair as normal. If the player fails to shoot her feet, they will need to find a way to press the action button to talk to her and convince her off drugs. [verification overdue]
xboxonepcps4 She may become nonassignable like Sturges.[verification overdue]
xboxonepc She might refuse to get in her chair just standing next to it. When the player tries to speak to her she will tell the player that she needs to sit down, no other interactions can be made with her. There are two possible ways to fix this: [verified]
xboxoneps4 Scrapping and rebuilding the chair may fix this bug. Once scrapped, the chair will become available to rebuild after waiting or sleeping for an hour.[verified]
pc By opening the console, selecting Murphy and typing setpqv ebe71 var_MamaInChair 1. [verified]
pc Sometimes the vision you get from her is not about the current quest, but refers to some older one. For example, during Hunter/Hunted, she might give you a clue to get the key for Kellogg's Diamond City house which corresponds to the already finished Reunions. [verification overdue]