Question: "What is the exception clause?"
Answer: The "exception clause" is Jesus' statement in Matthew 5:32 and 19:9 "except for marital unfaithfulness." It gives an "exception" for remarriage after a divorce being considered adultery. Matthew 5:32 reads, "But I tell you that anyone who divorces his wife, except for marital unfaithfulness, causes her to become an adulteress, and anyone who marries the divorced woman commits adultery." Similarly, Matthew 19:9 reads, "I tell you that anyone who divorces his wife, except for marital unfaithfulness, and marries another woman commits adultery." So, what precisely is "marital unfaithfulness," and why is it an exception to Jesus' statement that remarriage after a divorce is adultery?
The meaning of Matthew 5:32 and 19:9 is clear. If a person gets a divorce and then remarries, it is considered adultery unless the exception clause is in effect. The phrase "marital unfaithfulness" is a translation of the Greek word porneia, the word from which we get our modern word "pornography." The essential meaning of porneia is "sexual perversion." In Greek literature around the same time as the New Testament, porneia was used to refer to adultery, fornication, prostitution, incest, and idolatry. It is used 25 times in the New Testament, most often translated "fornication."
The meaning of porneia in the New Testament seems to be the general concept of sexual perversion. Other Greek words are used to refer to specific forms of sexual perversion, such as adultery. With this meaning in mind, according to the exception clause, any participation in sexual perversion/misconduct is an exception to Jesus' statement that remarriage after a divorce is adultery. If one spouse commits adultery, or any act of sexual perversion, and a divorce results, the "innocent" spouse is free to remarry without it being considered adulterous.
Please understand, though, that the exception clause is not a command for divorce and/or remarriage. Jesus is not saying that if marital unfaithfulness occurs a couple should divorce. Jesus is not saying that if a divorce occurs due to marital unfaithfulness, the innocent spouse should remarry. At most, Jesus is giving allowance for divorce and remarriage to occur. In no sense is Jesus declaring divorce and remarriage to be the best or only option. Repentance, forgiveness, counseling, and restoration are God's desire for marriages damaged by unfaithfulness. God can and will heal any marriage in which both spouses are committed to Him and willing to follow His Word.