A marriage in which one of the spouses in unbaptized is called a “natural marriage.” It is different from a sacramental marriage in that a natural marriage can be dissolved, whereas a consummated sacramental marriage can never be dissolved (canon 1141) except by death.
While a natural marriage can be dissolved, it is not the divorce that dissolves the marriage.
If there is a marriage between two unbaptized persons and one of them wishes to become baptized and the other refuses to be baptized and/or remain in the marriage, this is called the Pauline Privilege (1 Cor 7:10-15; canon 1143). In this situation the new marriage dissolves the previous marriage, but the Church must verify that the proper circumstances are present before the new marriage can proceed.
In a natural marriage where only one of the spouses is unbaptized and the baptized spouse is not a Catholic, and one of the spouses wishes to become a Catholic and the other spouse refuses to remain in the marriage then the Church can dissolve the natural marriage. This is called the Petrine Privilege or “privilege or favor of the faith.” In this situation it is not the new marriage that dissolves the natural marriage but the authority of the Roman Pontiff.