The Greek verb thanatoo means to put to death, to kill, or to cause death. In the New Testament it carries both its literal sense (physical death) and a powerful theological sense (putting to death the deeds of the body, dying to sin).
Romans 8:13 is perhaps the most important theological use: 'If by the Spirit you put to death (thanatoo) the deeds of the body, you will live.' This verse makes the mortification of sin (putting it to death by the Spirit's power) a mark of Spirit-filled life. The same word is used for Christ being 'put to death in the flesh' (1 Peter 3:18).
Theologically, thanatoo teaches the radical nature of Christian discipleship: sin must be killed, not managed. The old self must truly die. This is not self-improvement but Spirit-enabled death to what would destroy us.