In order to understand this story, there needs to be some context. Believing in witches had existed since the 1300's, and at that time, in 1689, life in colonial New England wasn't very good. There was a recent smallpox epidemic, citizens were constantly afraid of being attacked by Native Americans, and tensions were rising with the citizens of Salem Village and Salem Town.
In January 1692, 9-year-old Elizabeth (Betty) Parris and 11-year-old Abigail Williams began behaving strangely and having uncontrollable outbursts of screaming. A local doctor diagnosed them with bewitchment, and many other girls began having violent fits. In late February, Paris' Caribbean slave, named Tituba, along with two other women, a homeless beggar and an elderly woman, were accused of bewitching the girls.
The three "witches" were brought before court, where two of the three people said that they were innocent, while the third, Tituba said that she committed witchcraft. She probably said this to prevent herself from further charges. A number of other people were accused after the word spread around New England that there was witchcraft going on in Salem. More people confessed and named other people connected to it.
In total, nineteen people were hanged because of this, seven people died in jail, and one man was pressed to death by stone when he wouldn't confess.
After the trial, there was a lot of controversy, as there should have been. Increase Mather, the president of Harvard College, urged that the standards of evidence for those witch trials should have been equal to those in regular court. In 1697, five years after the Salem Witch Trials occurred, the court deemed the trials unlawful, and the judge presiding over the case publicly apologized. Overall, it was a very bad case, where fearful citizens wrongfully accused and executed innocent citizens because they were suspected of witchcraft.
Note: Arthur Miller wrote about this event in his famous play The Crucible.