Gran is the healer in the town of Levinshir. Kvothe notices that she has at least the same ability as many physicians who studied at the Medica. Her knowledge of herb lore, in particular, is quite vast and detailed.
In the Plot Edit
Gran's part in the plot is small but important in that she engages a great and altogether important change in Kvothe, after talking to her about his previous act of killing the Fake Edema Ruh Troupe. This enacted a change in his thought proccess, no longer was he so innocent (to the degree that he was before) and began to shape himself into a person more similar to the Amyr.