In the movie the Exorcist (1973), Father Karras dies by throwing himself out of a window. He takes this action in order to purge the demon (Pazuzu) from his own body since he had coaxed it out of young Regan MacNeil's body. When Karras in the end hits the foot of the stone steps, it is clear that both he and Regan are now free of Pazuzu, the demon.

What has happened was not suicide. Karras took on the demon, freed Regan, saved her life … at the cost of his own. The accolade of self-sacrificial hero directly goes to Father Karras. The demon lost. Human love (divine love) won.

At first, Father Karras was just a Jesuit psychiatrist suffering his own crisis of faith. So he accordingly had to search for the proof needed to perform the exorcism. During his investigation he came to realize that there was no better way for God to prove his own existence than to reveal the foul presence of a demon. During the exorcism, the demon frequently brought up Karras's mother and the matter of her death. It was pointed out that Karras was not present to see his mother actually die; this greatly troubled Karras emotionally.

In his fictional biography, after being born in 1935 to a Greek family, Father/Dr. Damien Karras S.J. over time became a psychiatrist, vocational counselor, and Jesuit priest. He served as a priest from July 1957 until his fight with the demon resulting in his harrowing and altruistic death.

More Info: en.wikipedia.org