This (unofficial) designation is in several ways inappropriate. It does not relate to any privilege as a special right of particular persons; moreover, the reference to Peter has no basis in the New Testament.
The term refers to divorce, on the basis of papal authority (the so-called potestas vicaria), of a non-sacramental marriage, including cases in which, at the time of contracting the marriage, one party was already baptized (half-Christian marriage). The marriage is dissolved by papal decree. The sufficient reason is in general ¶ the salvation of the soul, no…