AUCKLAND, New Zealand—Vince Cocurullo, the mayor of Whangarei District Council in New Zealand’s North Island, said he resonated with the meaning behind the name “Shen Yun.”

“Absolutely the divine dancing, every dance has been absolutely divine,” he said.

Shen (神) is a term that means divine being, indicating the myriad deities, Buddhas, and Taoist immortals in Chinese spiritual traditions, while Yun (韻) means rhythm and conveys a person’s entire bearing.

Combined, Shen Yun means “the beauty of divine beings dancing in the heavens,” according to the company’s website.

“The colors, the dance—it’s actually impressive to see guys so light on their feet,” Mr. Cocurullo said.

Shen Yun aims to revive this culture, which is something audience members can see and feel throughout the performance.

“I don’t think it is well known in the West,” said Anca Suciu, a physician who watched Shen Yun at the Kiri Te Kanawa Theatre, Aotea Centre in Auckland, New Zealand, on Feb. 22.

Ms. Suciu said she grew up in communist Romania, where the country did not recognize its roots and culture, similar to communist China.

“For 50 or more years of political ideology, there was so much restraint where we are losing touch with the underlying culture,” she said.

“I can understand how it is to lose [generations of cultural understandings], and unfortunately the way that [Chinese] culture is [perceived] outside because of these constraints.”

“The technique was amazing and just the discipline of all the dancers and the musicians as well. And even just the backdrops were wonderful, just utilizing the backdrops as far as jumping into it, and that was just fantastic,” said Ms. Hetaraka-Furey after watching Shen Yun with her husband Christopher at the Kiri Te Kanawa Theatre, Aotea Centre in Auckland, New Zealand, on Feb. 22.

“The music and the expression of the dancers are more than enough to tell the story. It was wonderful,” she said.