According to Wikipedia, addiction is a state characterized by compulsive engagement in rewarding stimuli, despite adverse consequences. For detailed information regarding how addiction occurs in the brain, please see http://en.wikipedia.org/wiki/Addiction.
Many of us can use substances or become engaged in activities without any significant problems. Some people, however, may experience damaging psychological and/or physical effects when their habit becomes an addiction. (from Medical News Today)
Addiction – there is a psychological/physical component; the person is unable to control the aspects of the addiction without help because of the mental or physical conditions involved.
Habit – it is done by choice. The person with the habit can choose to stop, and will subsequently stop successfully if they want to. The psychological/physical component is not an issue as it is with an addiction.