Abigail Williams, one of the main antagonists in Miller's play "The Crucible", is given the power by those wishing to prosecute and find guilty the witches of Salem.
While it is not that she, alone, has the power, persons (during this period) simply had to accuse a person of being a witch to have power in the eyes of the officials.
During the Salem witch trials, when people were accused of being witches they were carefully questioned about their knowledge of the "practices." This was important because it only took the testimony of one person to convict another of witchcraft.During this period, anything which challenged the Church was deemed sinful. Therefore, anyone who took part in practices which the Church deemed wrong could easily be accused of witchcraft. Given that Abigail was out for revenge (and no one knew of her affair with John Proctor), a popular reason to accuse, she was easily believed. The hysteria which took place also added to her ability to accuse at whim.