What did the Apostle Paul mean in 1 Corinthians 7:14?

Sanctified and holy both mean "to be set apart". And so as long as there is a believing spouse in the household, there is also a presence of the Holy Spirit in that household. And the Spirit works to draw sinners to Christ and set them apart unto Him through faith. The same principle applies in the work place. If there are believers in the workplace, they constitute an active presence of God's Spirit to come alongside the unbeliever.

There are three prepositions used in the bible that describe the proximity of the Holy Spirit in relationship to an individual. There is "with", which describes the Holy Spirit's ministry in the life of the unbeliever. There is "in", which describes the ministry of the Holy Spirit in the believer. And there is "upon", which describes the ministry of the Holy Spirit in a person who is totally surrendered to Christ and filled with the Spirit. And often times this "upon" ministry in one individual constitutes the "with" ministry in the life of an unbeliever.

And so the unbelieving spouse and children are both in a position to be drawn unto Christ, and eventually set apart unto Him, by the Holy Spirit's presence in the home via the believing spouse. And without that presence, then the children are going to naturally gravitate away from the things of God, hence the use of the term "unclean".

Corinthians 7 14

Many people see that "sanctified" term and they get the impression that it says "saved" or "justified" instead - which is not what it says. Sanctified means to be set aside for a specific purpose, just like a Christian is in relation to Christ and the world (John 17:17).

Context is key. Based on the previous chapter, 1 Cor. 6:15 talks about the vice of being joined to a harlot. A Christian being joined to an unbelieving spouse is still a legitimate union based on the faith of the believer, rather than being equivalent to being joined to an harlot.

Beyond this, fellowship is even more important. I'm sure you can understand, especially in the early church, that you cant just have any lost person coming to every type of gathering a Christian has (not talking about outreach here), for safety and testimony reasons, and Christians were not to fellowship with peolpe in the world. Note Paul's instructions in chapter 5 of this book.

1 Corinthians 5:9-13

9 I wrote unto you in an epistle not to company with fornicators: 10 Yet not altogether with the fornicators of this world, or with the covetous, or extortioners, or with idolaters; for then must ye needs go out of the world. 11 But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner; with such an one no not to eat.

12 For what have I to do to judge them also that are without? do not ye judge them that are within? 13 But them that are without God judgeth. Therefore put away from among yourselves that wicked person.

A the spouse of a saved person would be set apart from the typical reason given in the passage to not have fellowship or company with a person. Therefore, that person could be involved in fellowship, child training, marital counseling, etc... for the sake of the believing spouse.

The point of the passage is not to say that the children become unclean if there is a divorce. Point is to say that if the believing spouse didn't sanctify the unbelieving spouse (if it didn't work that way), then the children would be unclean.

Well lets look, Why should a Christian try to keep their marriage to a non-Christian together? Because God can be glorified in such a marriage, and do a work through the believing spouse to draw the unbelieving spouse to Jesus Christ.

Sanctified, in this context, does not mean that the unbelieving spouse is saved just by being married to a Christian. It simply means that they are set apart for a special working in their lives by the Holy Spirit, by virtue of being so close to someone who is a Christian.

The passage here Martin is not dealing with salvation or sanctification (being made holy before God) at all. Instead, it is dealing with the marriage relationship between a husband and wife, and this and the following passages deal specifically with the issue of a Christian who has an unbelieving spouse. Paul taught that Christians should not be “unequally yoked” (2 Corinthians 6:14) with unbelievers. Here in this passage, he clarifies that if a believer is already married to an unbeliever they should remain married as long as the unbeliever consents to do so. The reason this would be allowable is that the marriage relationship would be sanctified (holy or set apart in God’s eyes) based upon the faith of the believing spouse. Likewise, the children of that marriage will be legitimate in the sight of God despite the fact that Christians are not to be unequally yoked with the lost.

Christianity was not around for all that long at this point in time, so one spouse

was becoming a believer while the other was not.

The other option was divorce, and God was against divorce. The person could not

help being married when they were an unbeliever.

This happens today also. One person becomes a believer. This scripture shows

that God values the marriage and the children of that marriage. This shows that

God keeps this marriage and the children because of the believer. All come under

His ways, His protection, His blessings because of that one person. We see this

again and again in the Old Testament where all are spared because of one

person. It shows the goodness of God. (Also, we read if the spouse is WILLING to

stay...so it's OK if the spouse wishes to leave, the unbelieving spouse). This is

very liberal thinking during that time period, so long ago now.

Even if the unbeliever should leave, the children already having been born in marriage are clean, remain clean.

However, the Christian is not bound to remain single should the unbeliever leave but may attain a divorce to marry again. This does not mean that the Christian has the right to force the unbeliever to leave at all, that would be a serious sin.

However, this "willing to live with" implies not only the will to live with but also the abstinence from violence toward that Christian in both physical, emotional, and economic ways.

That being said, all couples experience troubles. That should not be construed as good enough reason to divorce.

So the unbeliever does not become believer by this sanctification; rather, it is the union of marriage that carries the mark of approval of God, this sanctification of their offspring, and their union.

Concerning Christian men married to unbelievers, Paul wrote: “If any brother has an unbelieving wife, and yet she is agreeable to dwelling with him, let him not leave her . . . For . . . the unbelieving wife is sanctified in relation to the brother; otherwise, your children would really be unclean, but now they are holy. For, . . . husband, how do you know but that you will save your wife?” (1 Corinthians 7:12-14, 16) The word “unbelieving” here does not refer to a wife who has no religious beliefs but to one who is not dedicated to Jehovah. She could have been a Jew, or a believer in pagan gods. Today, an elder might be married to a woman who practices a different religion, is an agnostic, or even an atheist. If she is willing to stay with him, he should not leave her simply because of differing beliefs. He should still ‘dwell with her according to knowledge, assigning her honor as to a weaker vessel, the feminine one,’ living in hopes of saving her.—1 Peter 3:7; Colossians 3:19.

9 If an overseer has children, he will exercise proper husbandly and fatherly headship in raising them “in the discipline and mental-regulating of Jehovah.” (Ephesians 6:4) In many lands the law gives both marriage mates the right to provide religious instruction for their children. In this case the wife may demand to exercise her right to expose the children to her religious beliefs and practices, which may include taking them to her church. Of course, the children should follow their Bible-trained conscience with regard to not participating in false religious ceremonies. As family head, the father will exercise his own right to study with his children and take them to meetings at the Kingdom Hall when possible. When they reach the age at which they may make their own decisions, they will decide for themselves which way they will go. (Joshua 24:15) If his fellow elders and the members of the congregation can see that he is doing all that the law allows him to do to instruct his children properly in the way of the truth, he will not be disqualified as an overseer.

Through Jehovah’s regard for the Christian, his (or her) marriage relationship with his unbelieving mate is not considered to be defiling. The cleanness of the sanctified one does not sanctify the mate as one of God’s holy ones, but the relationship is clean, honorable. The unbelieving mate has a fine opportunity to receive benefits from observing the Christian course of the believer and may himself be saved. (1Co 7:14-17) Because of the ‘merit’ of the believer, the young children of the union are considered holy, under divine care and protection—not unclean as are children who do not have even one believing parent

It means that the saved/believing spouse, if they have influence in the home, act kind of like an umbrella which enables others to be blessed. If you were a flower growing next to a water sprinlker, you'd get blessed with water when it is turned on even if the water was meant for the grass..