The Olympic Coven is the official name of the Cullen family. The coven is formed basically due to the sheer size of the family, which is rare within the vampire world. The Coven symbol allows others to recognise where and who they belong to and are with. Since the Cullens are 'vegetarians', only feeding on the blood of animals, and never on that of humans.
 
Another coven exists by the name of Denali. In Breaking Dawn, this coven is described by the vampire Tanya as a sort of extended family.  Members of the Denali Coven also feed on animal blood, and are very close to the Cullens. It is unknown whether they, too, wear the crest.