The Afton family is the main focus of the FNaF storyline. It is currently unconfirmed how many people there are in this family, but it is speculated to be either 5 or 6 members.
William Afton is the main Purple Guy, and the murderer of the children who possessed the animatronics. He was killed when he saw the ghosts of his victims, after being chased by them for a while, he fled into the Springtrap suit. The suit malfunctioned, killing him, and his spirit possessed the animatronic subsequently. He survived the fire of FNaF 3, and was one of the animatronics destroyed in the final fire of FFPS.
Not much is known about William's wife, including her name, but she is speculated to be possessing Ballora.
The Bully Brother, as his name suggests, bullies his younger brother (Crying Child) because he is scared of the animatronics. But his bullying goes too far when he shoves his younger brother into Fredbear's mouth, and his younger brother is killed.
The Bully Brother has been speculated to be Michael Afton, so he is the reason why there could be either 5 or 6 members of the Afton family.