During the period in time which "The Crucible" takes place, Puritanism was the predominant religious following.
The government of Salem in 1692 was a Puritan theocracy. In other words, the town was under the unbending authority of the church.
Witchcraft was heavily frowned upon by the church. It was looked at as being an alliance with the Devil, something the Church looked upon with hatred.
Therefore, given that Salem was a God-fearing state, any questionable activities which would lead one to believe that there were persons involved in behaviors associated with the Devil were looked upon with fear.
The work itself plays upon the idea of hysteria. Once the initial accusations were made against one, the ability to accuse others in order to force payment for personal wrongdoings was inevitable. The town burst at the seams with accusations made simply to force the courts to, unknowingly, clear personal feuds.