For a married woman is bound by law to her husband while he lives, but if her husband dies she is released from the law of marriage.  Accordingly, she will be called an adulteress if she lives with another man while her husband is alive. But if her husband dies, she is free from that law, and if she marries another man she is not an adulteress. (ESV)
The time of the Early Church was a challenging one. For the Jews who had been given the Law this new covenant relationship with God through Jesus Christ was a challenging one. A typical Jewish boy would have not only been taught the Law from his earliest years but would have memorized large portions of it as well.
The Law had such a bond on the people of Israel that Paul is able to use this illustration from marriage. Imagine that you had such a relationship with the Law of God. To set it aside for a new way of understanding your relationship with God would feel like a divorce. It would almost seem like you were cheating on the Law in order to embrace salvation by the grace o God, not by works.
In some ways we are very handicapped in our understanding of what the Jewish people would have gone through. Sadly, our view of marriage is so inadequate that we have a hard time with Paul's illustration in these verses. In our society marriage is rarely honored and divorce is easy and prevalent.
Paul reminds his readers that marriage binds a woman to her husband only as long as he lives. When the man passes away she is free to remarry. This passage is simply intended to show that it is ok for the Jews to embrace Christ. The Law had them bound, but because Jesus fulfilled the Law and died, the bond of the Law died with him. They can now follow the resurrected Savior as a new husband.
Have you fully embraced Jesus Christ as your new "husband?" Let everything that is in your old life go. Give yourself fully to your Savior.