The sacrament of marriage. There is a (blech!) ok there is a sacrament of marriage and a civil marriage. the sacrament of marriage or the marriage in the church never took place when it is annulled.
sigh.
The Catholic Church has seven Sacraments, as part of our faith tradition, one of which is the Sacrament of Matrimony, in which two people, who have made an eyes wide open decision to join themselves together, in Covenant, forsaking all others, and keeping each other until death, stand before a priest and make that promise to each other. The priest, and any other person there is simply a witness to the promises made, and the Sacrament being conferred by God. But in order for ANY Sacrament to be 'valid' in the eyes of the Church, BOTH parties have to be fully cognizant of, and in agreement with, all of the requirements of that Sacrament. If one or both parties in the marriage has no intention of living according to the vows they are making, that Sacrament is not valid. The party who HAS made that commitment, and lives according to the Sacrament hasn't committed any sort of sin, but technically, isn't really 'married in the Church', even though that person is married, according to the laws of the government, and even though that may also not be known by any of the parties involved on the Church side of things.
When a decree of divorce is issued by the state in which a couple live, legally, their lives are now separate. Any children who may have been born of that union are still considered 'legitimate', even though, legally, their parents are no longer married. Remember, it is the government that confers 'legitimacy', by virtue of the marriage certificate issued by the state. There are some folks who were not married in a church, who have kids, and their kids are certainly 'legitimate'. This is why the idea that if there is an Annulment, the kids from that marriage are 'bastards', is so ridiculous!
Because the Sacrament of Matrimony is strictly a Catholic thing, if there is a divorce, and one of the parties wishes to marry again, there has to be an investigation into the validity of the original Sacrament. In some cases, it's found that one or both of the parties never intended to follow the rules of the Church regarding the Sacrament of Matrimony; making the decision freely and without reservations, being faithful to one another, raising kids in the Church, etc. There is a Tribunal that will study the petition, interview witnesses, and make the determination whether or not the Sacrament was, in fact, valid, or not. If the Sacrament is deemed invalid, then a Decree of Annulment is issued, and the parties are free to marry again. And those who have already married again, are now able to partake in the Sacrament of Eucharist, which is withheld if someone is re-married outside the Sacrament of Matrimony.
There are many who have been told that just simply being divorced meant they could not receive the Eucharist. This is INCORRECT! It's not the being divorced that is the issue, it is a re-marriage without the first marriage being annulled, that is the issue. I once met a woman in a parish renewal course who had stayed away from Communion for almost 20 years because some idiot priest had told her now that she was divorced she couldn't receive. When she mentioned this, several of us in the meeting told her that was wrong, but I told her I'd talk to the Pastor myself to get an answer for her. When I talked to him, he told me to have her call him. She did so, and a couple of weeks later, I saw her go up to receive Communion, and she looked so happy, I almost cried. Frankly, I was amazed that she had stayed in the Church for all those years, and attended Mass faithfully, denying herself the ability to receive Communion.
So, short story long; that's the reason behind the difference between a civil marriage and the Sacrament of Matrimony, and the mechanism behind dissolving each.