I have not read the play, but show this film annually in my senior classes when we are studying the Anglo-Saxons.
Henry II is portrayed as a beligerent and self-centered king, which I have no doubt was true based on what I've read of his history. He displays his power in his family (belittling his children, chiding his wife and mother) and in his country (brow-beating servants, noblemen, church officials, and even his friend, Thomas Becket).
Henry is constantly at odds with the power of church and its wealth, since at this time in England, the church was every bit as powerful as the head of state. Henry was determined to get money from the church to fund the wars and building projects during his reign.
One way Henry thought he could get around the issue of Church vs. State was to appoint his best friend, Thomas Becket, to the highest church position available in England: Archbishop of Canterbury. Of course, Henry does not consider that this appointment will alter Becket's relationship with Henry. Becket, however, is a man of conscience and morality. He truly worked hard at being an excellent Archbishop and to serve the people of England well. He gave the poor the cloak off his back and the shoes from his own feet if they were in need which endeared him to their hearts.
Becket would not betray his job at Archbishop to serve Henry's needs. The breaking point came when one of Henry's noblemen committed a crime against a man of the church and Becket demanded that the nobleman be punished for his misdeed. Henry refused, as it was not politically prudent. Therefore, the tension between the two former friends grew until such time that Henry declared, "Won't anyone rid me of this cursed bishop?" Consequently, several of his own knights traveled to Canterbury and murdered the Archbishop in the cathedral. To this day, there are still pilgrimmages to the cathedral to pay homage to the man who served them so selflessly.
thank you so much for this answer it was very helpful ^_^