Geoffrey Swan was the husband of Helen Swan; the father of Charlie Swan, and the grandfather of Bella Swan. He became the grandfather-in-law of Edward Cullen after his marriage to Bella, and the great-grandfather of Renesmee Cullen.
It is mentioned in The Twilight Saga: The Official Illustrated Guide that he and Helen assumed they could not have children, so Charlie was an unexpected, but very welcome, surprise. He and Helen were in their mid-40s when their son was born.
By the time Charlie reached adulthood, their health began to deteriorate and worsened through the years: Geoffrey's mobility was being curtailed by severe arthritis and Helen suffered from Alzheimer's disease. Their conditions worsened when his daughter-in-law, Renée was pregnant with Bella. He needed Charlie's help with Helen every day. When Renée left with Bella, Charlie stayed in Forks to take care of his parents.
Four years after Charlie's and Renée's divorce, he passed away, and then his wife, too, leaving their son alone to deal with his life.
Life and Death: Twilight Reimagined
In Life and Death: Twilight Reimagined, Geoffrey has a grandson named Beau Swan. Beau became a vampire near the end of the novel and had to fake his death. A funeral was held and his empty casket was buried next to Helen and Geoffrey's.