It is not possible to marry the same person twice without a divorce. When people are legally married with an issued marriage license that's been signed, they cannot get married again.
If a couple wants to remarry without first getting a divorce, they can hold a ceremony and go through all of the motions of a wedding. For many couples, this is referred to as renewing the vows. To marry a person again legally, they would have to go through the process of divorcing for the second marriage to hold up in court. Renewing the vows is an excellent way for two people to reaffirm their love and commitment for each other. This second wedding can even be done in a church with a pastor, family and friends in place.