The word translated "covetousness" here is the Greek word pleonexia. It is an ugly word describing an ugly sin. It is ugly because it is idolatry and destructive. Lexicons describe pleonexia as "the insatiable desire to have what rightfully belongs to others." It suggests ruthless self-seeking and an arrogant assumption that others and things exist for one's own benefit.
Covetousness is idolatry because it puts self-interest and things in the place of God. A man sets up an idol because he desires to get some pleasure or satisfaction from it. So he serves to get, which is idolatry. The essence of idolatry, then, is to get for the self. Christians, though, must give themselves to God, and we do it by yielding to Him in obedience to whatever He says.
Colossians 3:5 says we are to "mortify therefore [our] members which are on the earth" (KJV). This does not mean merely to practice an ascetic self-discipline. It is a very strong word, meaning "to kill." The Christian must kill self-centeredness. He must radically transform his life, shifting the focus from himself to God. This is exactly what Jesus taught in Matthew 5:29-30. Everything that keeps us from fully obeying God and surrendering to Jesus Christ must be spiritually excised. The tenth commandment, like the first, serves as a governor, controlling whether we keep the others.