If accompanied by other enemies it only uses normal attacks and its special, Mysterious Dance, which puts a party member to Sleep. If they are the only enemy present they use Fira, Blizzara, or Thundara every turn, doing heavy damage to the party if group-cast and likely killing a party member instantly if cast on a single target.
Locke can steal a Thief's Knife from them. The Ragnarok summon can turn them into the powerful Miracle Shoes relic, and because the random encounters in Zozo remain the same in both the World of Balance and the World of Ruin, and the enemies in Zozo are weak by the point in the game the player gets Ragnarok, they provide a safe and easy way to attempt to stock up on Miracle Shoes.
A veil dancer is a performer who preforms veil dancing. Such dances occurred in the ancient western world such as Persia. It is similar to belly dancing, but involves the use of a veil. One famous veil dance is the Dance of the Seven Veils, performed by Salome before king Herod Antipas.
Veil Dancer's older name refers to moshing or slamdancing, a style of dance in which participants push or slam into each other, typically performed to "aggressive" live music.