In  the “Catechism of the Catholic Church,” Part Three, IV.  Offenses Against the Dignity of Marriage, Divorce, 2383, it states, “If civil divorce remains the only possible way of ensuring certain legal rights, the care of the children, or the protection of inheritance, it can be tolerated and does not constitute a moral offense.”  Will you explain this statement specifically in reference to legal rights and protection of inheritance?  

The section you cite appears in the Catechism’s presentation of the sixth commandment, “Thou Shalt not commit adultery.”
 
When a couple gets married in the Church, there are civil legal effects and canonical (Church) effects to the marriage.  The “ensurance of legal rights, the care of the children, or the protection of inheritance” is a broad category, and a specific listing of all situations where a civil divorce would be justified is not practical here.  So let me illustrate for you a common case where civil divorce would be justified because it would ensure legal rights, care of the children, and protection of inheritance.  It’s the case of a spouse who has become an addict, whether to drugs, gambling, or alcohol.  Sadly, in this case, the chaos caused by the addict could ruin the entire family.  That is not fair.
 
In this case it is possible for the wife (or the husband, as the case may be) to seek a divorce in civil court to protect herself and her children.  In pursuit of his pleasure, and addict could leave the family destitute.  So, a civil divorce would at least allow her – in most states – to protect half of the family’s assets from further erosion.
 
In this case, while the couple has been granted a civil divorce with attendant consequences for the family assets, it does not mean they are no longer married in the eyes of the Church or in the eyes of God.  If they have a reasonable doubt that their marriage was valid in the first place, they have a right to petition the competent ecclesiastical authority (their bishop) to review their marriage and determine if it is null. If in fact there was a serious defect at the time of marriage, the bishop’s tribunal will declare the marriage null.  That is an annulment.