This has always been one of the more important teachings regarding sin and establishing our theology. It was thought that when one person sinned that sin was on the head of all people in the community. All people would be punished for that sin.
It was also thought that if the parents sinned in their lifetime their children would also carry the burden of that sin in their lifetime. Ezekiel corrects the theology and our understanding. He teaches that each person is responsible and accountable for the sin they committed. The sinner must make restitution for the sin. The sin is not transferrable to others.
As the sin is not transferrable it does not mean that the children are not negatively impacted. For example, alcoholism. The parent who was an alcoholic impacts his children in a negative manner. The alcoholics nature is learned by his children. They now will tend to become addicted to alcohol. And this becomes then a generational problem. Alcoholism is transferred from one generation to another until the cycle can be changed. Psychology has proven this many times.
Breaking these generational issues is extremely difficult. Other addictions would be gambling, abusive behavior in the home, sexual addictions, and others. It would be good for people to reflect on the lives of their parents and discern what addictions may have been transferred. Then determine what steps are needed to break these generational issues.
May the Lord bless you in the name of the Father and of the Son and of the Holy Spirit. Amen