Jenny Jackson is Annie's mother, and the first wife of Charles Jackson. She appears briefly in the beginning portion of the series alive, but passes away a few episodes later due to an illness.
Jenny was quite active in Annie's life, especially in her adult years after her children were born. She seemed to be around more often during the early years of the grandkid's lives. It's shown in a few episodes as well as even mentioned that she had quite a bond with Lucy. She's also shown to have quite a bond with her daughter, Annie, even appearing to her twice after passing away.
Jenny appears with her husband in the pilot. She shares bad news with her daughter, then leaves in the following episode. She soon returns, but passes away in the home of her daughter, but not before appearing to her in a dream and saying goodbye to her. This is the first time she appears to her daughter after passing away, showing a close bond with her.
Jenny goes onto make several more appearances after death. She appears once in a video. She appears again as a ghost to encourage Annie when she's about to give birth to the twins. She makes another appearance in a flashback when Annie starts thinking about her upon realizing Lucy has grown up. Later, Jenny appears as a ghost to her granddaughter, Lucy to warn her of an upcoming challenge. This shows another great bond between the two. Her final appearance is in heaven.