The Greek word underlying "covetousness" is pleonexia, which means "the desire to have more." This is among the ugliest of sins because it involves idolatry as well as its effects on others. The Greeks defined it as "the insatiable desire to have what rightfully belongs to others." It is further described as "ruthless self-seeking," the kind of attitude that the arrogant and callous person has, assuming that others and their things exist for his own benefit.
The desire for more money can lead to theft; the desire for more prestige, to evil ambition; the desire for more power, to tyranny; the desire for a person's body, to fornication and adultery. Paul identifies covetousness as idolatry because, in the place of God, it puts self-interest for illicit things. A man sets up an idol in his heart because he desires to get something from it. So he serves it to get that something rather than to obey God's commandment. That, very simply put, is idolatry.
The essence of idolatry is to get for the self in defiance of God. However, we have to give ourselves to God if we want to overcome illicit desires. Paul says to "mortify" (KJV) or "put to death" (NKJV) whatever is sinful. That does not mean to practice ascetic self-discipline—it means to kill. The Christian must kill self-centeredness. In his life, he must make a radical transformation, a shift of the center of his life. It is the same principle as described by Matthew 5:29. Everything that keeps a person from fully obeying God and surrendering to Jesus Christ must be surgically excised from his conduct.
The tenth commandment, then, has a function similar to the first. They both act as governors, controlling whether we keep the others.