The three were part of the group of girls/women who were dancing in the forest at the beginning of the play, setting off the action.
Tituba, Parris' slave from Barbados, is accused of talking to the Devil himself. In Puritan society, the forest was seen as a place where evil regularly takes place. (Realize at this point, there was little exploration beyond the Massachusetts Bay Colony in that area of the country, so the forest was a mysterious place) When the girls realize they were caught dancing, and perhaps calling up dead souls, they blame Tituba for leading them.
Abigail is one of the main characters in the play. She is Reverend Parris' niece. After being fired as a servant at John and Elizabeth Proctors' home for having an affair with John, Parris takes her in. Her desire to be with John leads her to begin the accusations, and the more accusations are made, the more she looks respectable, because Puritan society felt that accusing others was a patriotic and holy duty. She begins to doubt her Puritan upbringing after her affair with John.
Betty is one of the first girls afflicted by "witchcraft". It is implied that her fear from being caught dancing in the woods leads to her "illness", but for the most part her role in the play is as a catalyst to direct the action. She spends much of her time laying in bed, probably to avoid being punished by her strict father, Reverend Parris.