This proverb stands at the end of a short section, beginning in verse 5, illustrating the progression of the sinful person in contrast to those who fear God. The opening verse describes both of these types of people making plans: The upright have good goals and mark out an ethical route to reach them, whereas the wicked devise devious ways to get what they want. The middle proverb, verse 6, describes the thinking and speech of each type: Evil people use and abuse others—often the good people, who seem to be easy pickings—to get their way, while the righteous trust in their integrity, which they have learned from following God's ways, to get them out of troubles.
Solomon concludes his short character sketch with a confident announcement of the fates of these two types of people. In fact, the sense of the verse is that these ends are sure and inescapable. While we realize that God could intervene and turn the evil person to him, and that the good person could be derailed and fall from his godly integrity, Solomon is speaking in terms of the general human condition. The percentages are high that matters will run their course along the lines he draws in this proverb.
He sees the end of the sinful person as "overthrown and no more," a rendering that most of the major translations follow exactly or nearly so. The illustration behind their being overthrown is of a "turning of the hand," that is, an indefinite catastrophe will take them away in a moment. They will be here today and gone tomorrow, swept away in a vicious flash-flood of ruin, whether physical, financial, or otherwise. In other words, the wicked are setting themselves up for spectacular failure.
That they are "no more" implies that they will vanish from the scene. They may seem so formidable and permanent, but the catastrophe reveals just how powerless they really are, and they disappear as if they were never there. Underlying this assertion is a sense of the long-term, that the family line of the wicked person will not last, that no dynasty will be built. Their evil will consume them in short while, as sinfulness is really a kind of slow-suicide.
The more positive side of the proverb is that those who stand fast in God's way will have long life and perpetuity in their family. Again, this is not always the case—certainly, some righteous people never marry, and other righteous people, though married, never have children. However, the general truth is that right living produces conditions that encourage health, long life, and good habits and traits that are passed down from one generation to another.
The thought in this verse is expressed in several places in Scripture, perhaps best in the second commandment:
For I, the LORD your God, am a jealous God, visiting the iniquity of the fathers upon the children to the third and fourth generations of those who hate Me, but showing mercy to thousands, to those who love Me and keep My commandments. (Exodus 20:5-6)
The effects of a person's sins reach down the next few generations and cause untold harm, yet the righteousness of a godly person can produce blessings in the lives of his descendants hundreds or thousands of years in the future (consider the example of Abraham and his faithfulness). If we want good things for ourselves and our children, the clear choice is to "fear God and keep His commandments" (Ecclesiastes 12:13).