You can be an ESO vet because you've hung around in the game for a long time.
You know its history, you know what the game has to offer, probably been a master crafter for awhile, tried the different things the game has to offer and know what part of the game you enjoy.
You can also be an ESO vet because you do veteran content. Know the mechs, know your role and know what's expected of you in a vet que.