Polynesian referred to anything originating from the Polynesian Islands on Earth, including the Polynesian people. Elements of Polynesian culture included luaus and leis. The Māori culture, which also belonged to that group, were known for their tribaltattoo art.
According to StarTrek.com, the scene of people seen traveling in a primitive ship in the Enterprise opening credits was meant to show ancient Polynesians, which the site notes were among the first to explore the open oceans in their outrigger canoes. (X)