The concept of a generational curse comes from the second of God's holy Ten Commandments.
You shall not make for yourselves any graven image, or any likeness of anything that is in the heavens above, or that is in the earth beneath . . .
You shall not bow yourself down to them, nor serve them, for I, the LORD your God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of those who hate Me . . . (Exodus 20:4 - 6, HBFV, see also Exodus 34:6 - 7, Numbers 14:7 - 19 and Deuteronomy 5:8 - 11).
Some see such a generational "curse" as being caused by an evil spirit who has the power to harass the descendants of a particular person who is prone to commit certain sins. Still others see it as being a general "spiritual inheritance" in nature. Such curses are not thought to have a connection with heredity-based problems like a tendency to abuse alcohol.
Those who are under a generational curse, it is argued, are prone to committing certain types of sinful behavior. Solutions to this type of penalty include having someone involved in a deliverance ministry "discern" the exact curse a person possesses. With this information the individual can then specifically renounce the curses against them. If it is believed that the cause is an actual evil spirit, the deliverance ministry will try to "cast it out."
What the last part of the second commandments means is that our Creator made us in such a fashion that parents who disobey him are not always punished themselves. Sometimes, the full results of their sin is demonstrated in the next four generations. However, we should always remember that God deals with individuals as well as with nations and societies, the fact of which He reminds us of through Ezekiel (Ezekiel 18:14 - 17).
It is also important to note that the "generational curse" or punishment that comes with breaking the second commandment is qualified with "of those who hate me." This means if the second, third or fourth generation repents and turns to God with their heart, he may change his mind and forestall any punishment.