An annulment was the rendering of a marriage null and void.
Tavnian law maintained that if one married another spouse in a legal Tavnian wedding ceremony, the first marriage was annulled. In addition, claim to any children the first union produced were automatically lost by the first spouse.
In 2372, Odo offered to marry Lwaxana Troi so she could keep the male baby she was having with Jeyal, rather than have the child be raised by other makes, as per their tradition. They would then annul their own marriage afterwards. (DS9: "The Muse")