An annulment is a declaration that a marriage was in fact invalid after an extensive investigation.
What is investigated is whether or not at the time of consent a valid marriage bond was created. It is not a divorce; it is a statement that the bond of marriage as it is understood by the Catholic Church was not made.
Why can the Catholic Church conduct such an investigation?
If you are Catholic, or you intend to marry a Catholic, the Catholic Church can perform such an investigation to determine your freedom to marry. The Catholic Church does not believe a person can divorce and remarry; the only option is to petition for an annulment to determine if a marriage bond exists as it is understood by the Catholic Church. If an annulment is granted, you are then free to marry in the Catholic Church. This process has no civil effects.
For more information you can visit the Tribunal of the Diocese of Phoenix.