A more thorough explanation:

accredulitare (uh-kred-yuh-luh-tair-ee), verb. [Law Latin] Historical. To clear oneself of an offense by taking an oath.

• In medieval times, a person accused of a crime might have to accredulitare in order to prove their innocence.
• John was accused of stealing from the church, but he was able to accredulitare by swearing on the Bible that he was innocent.

These examples illustrate how accredulitare was used in the past to clear oneself of an offense by taking an oath. In medieval times, when the legal system was less developed, oaths were often used as a way to determine guilt or innocence. By swearing an oath, a person was essentially putting their reputation and honor on the line, and if they were found to be lying, they would suffer severe consequences. Accredulitare was one way to use this system to clear oneself of an accusation.