Edith was on Tris' dad's side. She was an ancestor who carried on the Prior name.
Caleb Prior points this out and also notes that many people of the Prior family were also Erudite and even a few Candor. There were seven generations from Edith to Tris, according to Caleb in Allegiant.
She says that the Divergent are needed to fight a war outside the fence, and that they can help people on the outside. Later on they find out this information was only partially correct.
Movie Portrayal Edit
Edith Prior is protrayed by Janet McTeer in The Divergent Series: Insurgent.