In Murder in the Cathedral by T. S. Eliot, martyrdom is related to the the theme of obedience and the internal warfare within man of flesh vs spirit.
The historical Thomas Becket was a friend to Henry II of England. So, when it came time for Henry to appoint another Archbishop of Canterbury, he figured if he made his friend the archbishop, then his friend would do what he said, i.e., place the wishes of the king over God. Prior to this time, Thomas’ life led Henry to believe that this would be the case. However, Thomas changed when he became archbishop. He became devoted to his spiritual life and took his position seriously. Soon, he was at odds with Henry over the rights of the Church vs the rights of the king. Thomas fled to France for awhile, to rally support for his cause, but he returned to England, and after that, he was murdered, in Canterbury Cathedral, by four of Henry’s knights.
Thomas did not plan to be a martyr, but he expected he would become one. He knew Henry very well and did not expect that the king would approve of an archbishop that placed God over the king. In the “Interlude” of the play and in “Part Two” while Thomas is preaching on Christmas Day, he tells the people that martyrdom is “never the design of man” but of God. God chooses who will be martyred for him – “the true martyr is he who has become the instrument of God.” Also, the “true martyr” is one “who no longer desires anything for himself.” He ends by telling the people that he is pretty sure he will be martyred.
Read about it here on eNotes.