DEMON POSSESSION — an affliction of persons in the New Testament who were possessed or controlled by demons (Matt. 4:24; 8:33; demoniac, NASB).
The New Testament gives graphic descriptions of the effect of demons on people. Some of the diseases which they caused included muteness (Matt. 12:22; Mark 9:17, 25), deafness (Mark 9:25), blindness (Matt. 12:22), and bodily deformity (Luke 13:10–17). But demons were not responsible for all physical ailments. The gospel writers frequently distinguished between sickness and demon possession (Matt. 4:24; Mark 1:32; Luke 6:17–18). Sometimes a problem caused by demons appears to have another cause in another situation (Matt. 12:22; 15:30).
In New Testament times demons were also responsible for some mental problems (Matt. 8:28; Acts 19:13–16). The ranting and raving that they produced probably should be included with mental disorders (Mark 1:23–24; John 10:20). Uncontrolled fits were another form of demonic affliction (Luke 9:37–42; Mark 1:26). Sometimes a demon also caused a person to behave in an antisocial manner (Luke 8:27, 35).
The method of Jesus and His disciples in casting out demons differed radically from the magical methods so often used in that time. Through His simple command Jesus expelled them (Mark 1:25; 5:8; 9:25). His disciples simply added the authority of His name to the command (Luke 10:17; Acts 16:18). Even some people who were not His followers invoked His power (Luke 9:49; Acts 19:13). In some instances prayer was necessary before a demon could be cast out (Mark 9:29).
By casting out demons, Jesus showed that the Kingdom of God—God’s rule in the affairs of mankind—was a present reality. This was also a clear demonstration of His power over Satan and the demonic forces of sin and evil in the world.
Youngblood, Ronald F. ; Bruce, F. F. ; Harrison, R. K. ; Thomas Nelson Publishers: Nelson's New Illustrated Bible Dictionary. Nashville : T. Nelson, 1995

Also see:

What does the Bible say about demon possession / demonic possession?