It legitimizes the marriage union, as well as their children being lawfully begotten. If one parent is a believer and the other is not, assuming they were married before one's conversion, then what becomes of the marriage union? Is it now lawful still, or unlawful since it is wrong to be unevenly yoked to unbelievers. But in this parculiar case, God has sanctified, or make holy, that unbelieving parent in a sense to not only legitimize the union, but also show that the children are not unlawfully begotten by such a union.
Before God they are both holy lawfully in that marriage institution and their children lawfully begotten.
It does not refer to an internal sanctification, or salvation, as many err to believe.