Final answer:
The devil informs Brown that his grandfather lashed a Quaker woman and his father burned down an Indian village, illustrating the devil's historic influence on Brown's family.
Step-by-step explanation:
The knowledge of Brown's ancestry provided by the devil is that Brown's grandfather had lashed a Quaker woman and his father had burned down an Indian village. This revelation by the devil occurs during Goodman Brown's journey in the forest, where the devil asserts his familiarity with Brown's family and shares these past deeds to show the connection between the family and the devil's influence.