Exorcism
In Catholic Christianity, exorcisms are performed in the name of Jesus Christ. A distinction is made between a formal exorcism, which can only be conducted by a priest during a baptism or with the permission of a bishop, and "prayers of deliverance" which can be said by anyone.
The Catholic rite for a formal exorcism, called a "Major Exorcism", is given in Section 11 of the Rituale Romanum. The Ritual lists guidelines for conducting an exorcism, and for determining when a formal exorcism is required. Priests are instructed to carefully determine that the nature of the affliction is not actually a psychological or physical illness before proceeding.
Mark 1
He then performs an exorcism on a demon possessed man. Curing people, especially possessed people, will be another major method Jesus uses in his mission in Mark. The demon recognizes Jesus as "the Holy one of God", the first time Jesus' supernatural opponents are shown to know his true identity. Jesus simply says "Be quiet, and come out of him!", healing the man with words alone. The people are amazed. This follows a path Mark often uses, that of a description of the affliction, Jesus' cure of the affliction, and then a demonstration of the cure to others. The power of Jesus' word over the demon might be Mark's way of trying to show to his audience, perhaps under the threat of persecution, that Jesus' message will overcome evil. By showing Jesus' teaching first before his exorcism Mark might be placing emphasis on Jesus' teachings as more important that any miracle he could perform.