The following is a practical illustration of what the New Testament teaches on fornication, marriage and adultery:
Joe and Lucy have sexual intercourse. Because neither Joe nor Lucy have ever been married, they commit the sin of fornication. If they repent, God will forgive them.
Joe and Janey get married and vow to love and cherish each other until death do they part. Joe and Janey have sexual intercourse and the marriage bed is undefiled. There is no sin in their sexual relationship because they are married. It is their commitment to each other for life that makes them married, not their having sexual relations.
Joe and Janey obtain a divorce from the state. Later Rocky finds Janey, a divorced woman. They make vows promising to love and cherish each other until death do they part. Their "marriage" is legal under the state, but God sees them as adulterers. Janey has already made a lifetime commitment to love and cherish Joe. If she has sexual relations with another, she violates her marriage covenant and commits adultery.
Rocky also commits adultery when he marries Janey because she is divorced from her husband. Jesus says, "Whoever divorces his wife and marries another commits adultery; and whoever marries her who is divorced from her husband commits adultery" (Luke 16:18).
Through the marriage vows, God has made Janey one flesh with Joe and what God has joined together let no man tear apart (Matthew 19:6). Janey was not free to marry Rocky. She is still married to Joe until Joe dies. If Janey and Rocky repent of their adulterous relationship and sin no more, God will forgive them.
If Janey wants to return to God's favor, she has two choices: remain unmarried, or be reconciled to her husband (1 Corinthians 7:11).
If Rocky wants to return to God's favor, he must separate from Janey. Assuming Rocky has never been married, he is free to marry another because his marriage to Janey was not marriage in God's eyes.
When Joe and Janey were married, they were young and foolish. Neither believed in Jesus Christ. Yet they did make a solemn commitment to be faithful to each other "until death do us part." There is a price to be paid on judgement day if that commitment is violated by marrying another.
Joe and Janey also bought a house and made a commitment to pay a 30-year mortgage. If the terms of that mortgage are not met, there is a price to be paid. They cannot just make the excuse that they were young and foolish and be relieved of their commitment. No, they will have to uphold their commitment or lose the house.
When we get married, it is not just a 30-year commitment. It is a commitment for life. As the years go by, we may find our spouse less than ideal. Many problems arise and we see other potential partners who are far better suited to our tastes. But unlike the 30-year mortgage, we cannot close out the first obligation (marriage) and step into a new one.
If you are married to an unbeliever, but they are willing to live with you, you are not to obtain a divorce (1 Corinthians 7:12-13). If the unbeliever departs, let them go. You are not forced to live with them (1 Corinthians 7:15). However, nowhere in scripture does it say that once they have departed, you are free to marry another.