William "Bill" ForbesII was a former Mystic Falls resident who returned to point out all the failings of the current Council’s attempts to keep vampires out of town, after discovering that his daughter, Caroline, is one of them.
Not much was known about Bill, except that he was once married to Elizabeth Forbes and had a child with her. He later left her, after announcing that he was gay. He lived with his new partner, Steven in Georgia.
Bill is not seen, but Caroline has mentioned him in You're Undead to Me that he has a boyfriend, once telling her mother Elizabeth that if she had guy problems, she would call her dad, because he was "successfully dating one." In Let The Right One In, Caroline tried to go to her father's boyfriend's daughter's birthday party, but on the way, discovered Vicki Donovan's body due to being stuck in the mud with her car.
Carol calls him to take care of Caroline who is revealed to be a vampire. After Carol Lockwood discovers Tyler Lockwood is a werewolf, she tries to tell Bill to let Caroline go, but he refuses. In the end, he enters a stone chamber where Caroline is locked up and she calls him "Daddy." He attempts to make Caroline associate human blood with pain, by exposing her to the sun without her ring so that she won't feed on humans, so he won't have to kill her. However, once night falls and he prepares to leave, his ex-wife and Tyler show up to free Caroline. He tries to stop Tyler, but Liz fires a warning shot at the wall. They take Caroline, who then cries saying that her father hates her. Later in the dungeon, Bill was held by his ex-wife and is visited by Damon who, after biting him to make sure he has no vervain in his system, erases his memory of Caroline's vampirism and tells him to leave the town immediately.
However, later that day he arrives to the council meeting and threatens to "out" Damon. He informs Damon that he can't be compelled, and said it's a sort of "human focus he's been honing for decades". Damon attacks Bill, most likely intending to finish him off, but Caroline, who still loves her father, shows up and feeds him her blood (even though he protests) before taking him out.
As he is about to leave, Caroline tries to assure Bill that she's fine and capable of controlling her urges, but he throws her arguments off.
In The Ties That Bind, Tyler calls Bill to help him fight the sire bond that he has toward Klaus. Bill orders Tyler to change into his werewolf form and threatens to decapitate him if he didn't change. In transition Tyler couldn't hold back and attacks Bill, almost killing him. Later, Meredith Fell heals him by injecting him Damon's blood. When Tyler came to apologize, Bill tells him that they'll continue the next day. He says that to break the sire bond, he has to turn every day.
In Bringing Out The Dead, Bill was killed by Alaric Saltzman (while he was taken over by The Darkness), who stabbed him to death and cut his throat while having vampire blood in his system. He woke up in transition but choose not to feed and turn into a vampire. Caroline was heartbroken by his decision and tried to convince him otherwise, but he remained firm in his beliefs that he would not turn into the creature he hates, though he is proud of the person Caroline is. He eventually died with his daughter and ex at his side.
Bill is very loyal to his daughter and his hometown. However, Bill proves to be cold, cruel and ruthless with the vampires, and the traitors of the town. During his stay in Mystic Falls, he tries to help Caroline and her vampire nature (self control).
In season 1 and 2, it is implied that she and her father were much better friends than she and her mother. Caroline mentioned that "he was the only one that could understand her". In season 3, Bill came back to Mystic Falls as he was informed that Caroline is a vampire. He tried to "train" her, by inflicting pain on her so she could "associate vampirism with pain", and control her urges better. He finally said he was doing this so he wouldn't have to kill her, meaning even though she is a vampire, he still loves her. Nevertheless, Caroline later admitted that she believed her father hated her for being a vampire and also said to her friend Elena Gilbert that she briefly hated her father for torturing her, even though his intentions were good. However, her love for her father never went away, for she became depressed and sad when he died.
Liz is Bill's ex-wife, and they presumably annulled their relationship when he confessed he is gay. Not to much of their past together has been revealed, but it can be deduced that they are on rocky terms, seeing as she was hostile towards him when they met again at the jail.
Bill Forbes is shown to have a relationship with the Town Council and threatened to expose Damon Salvatore to them. Not much is known on how involved he really is with the council.