Dear Francis:

The Pauline privilege is based on St. Paul's scripture:

To the married I give charge, not I but the Lord, that the wife should not separate from her husband ... and that the husband should not divorce his wife. To the rest I say, not the Lord, ... But if the unbelieving partner desires to separate, let it be so; in such a case the brother or sister is not bound. For God has called us to peace. (1 Corinthians 7:10-15, RSV)

The Pauline Privilege can only apply to couples who were both unbaptized at the time of their marriage, in which later one of them converts and is baptized while the other does not convert in the course of the marriage.

In such a situation, if the unbelieving spouse leaves the marriage, the marriage can be dissolved under canon law. This allows the believing spouse free to re-marry. This applies only if the unbelieving spouse leaves the marriage.

The Pauline Privilege differs from divorce in that it leaves the baptized spouse free to remarry. It differs from annulment because the Pauline Privilege dissolves a valid actual marriage, in favor of the faith of the baptized spouse, where annulments declare that a marriage was invalid from the beginning.

There is also a Petrine Privilege, similar to the Pauline Privilege. The details of this are rather complicated, but the Archdiocese of Chicago website give a basic explanation:

A Petrine Privilege or Privilege of the Faith is a dissolution of marriage in which at least one of the parties to a previous marriage was non-baptized throughout the entire duration of their married life. If the petitioner is the non-baptized party or was baptized in another Christian church, he or she must either wish to be baptized or received into the Catholic Church, or seek to marry a baptized, practicing Catholic. If the petitioner is a baptized Catholic who was married to a non-baptized person, he or she must either wish to enter into marriage with a baptized Christian, or promise to enter marriage with a baptized Christian in the future. Privilege of the Faith cases involve a special petition to the Holy Father and are decided in Rome.

God Bless,
Bro. Ignatius Mary