The title simply states what happened: Thomas a Becket was murdered in Canterbury Cathedral.
Eliot's play is based on real events. In the twelfth century, England's King Henry II clashed with the Archbishop of Canterbury, Thomas. The two had been close friends, and Henry thought that by making Thomas the most powerful church leader in the country, he would not only control the secular government but also the church. But being elevated to the highest church post caused a change in priorities for Thomas.
At that time, if a priest of other member of the clergy committed a crime, he could not be tried in a civil court. Only the church could decide guilt or innocence and assign punishment. Henry thought Thomas would agree to changing that tradition, but Thomas stood firm and opposed Henry. In a fit of rage, Henry is supposed to have said, "Will no one rid me of this turbulent priest?" That's when three knights decided it would be to their advantage to kill Thomas, and that's what Murder in the Cathedral is all about.