Great Grandpa Ziggy is Rose Nylund's great-grandfather, presumably from her father's side of the family. He was an inventor, and developed the first and the only low-voltage meter that could detect what kind of a center a piece of candy had.
In the episode A Long Day's Journey Into Marinara, Angela Vecchio arrives and tells her that she's not tired when Dorothy Zbornak offers a place for her to nap in after a long trip. This prompts Rose to tell a story, about how her father used to bring the whole family to Great Grandpa Ziggy's house. She was cut off just as she was about to tell the story when Angela says that she does need a little rest, followed by Dorothy, Sophia and Blanche. Rose warns the others that she'll tell the story as soon as they get up. The others return, unwillingly, to listen to her story.