Unfortunately, many pieces of art have perished since the discovery of Polynesia in 1500, as missionaries arrived and waged war with the native inhabitants. This is sad, as Polynesians had a developed tradition of tattooing, and actually the word "tattoo" derives from a word of theirs, meaning "to strike".
Speaking of Polynesian tats, we can differentiate between two basic kinds of them: the Enata, and the Etua. Enata are natural designs that represent a person's standing in the society, deeds, origins, occupation, etc. So a fisherman most likely received a tattoo which protected him from sharks and showed his occupation.
The second kind - Etua tattoos - carry a much deeper meaning, which can be religious and magical. These designs could show reverence to particular persons inside the tribe or could serve as a charm, by which gods gave the wearer luck.
Of course in modern tattooing circles the old meanings are not that important, as most of us don't have anything in common with Polynesian culture. They look good enough though for many people to opt for a tattoo like this. It especially fits on the arms, sometimes reaching to the chest. The design consists usually of circles, lines and knots which go in line with each other, sometimes bending away from each other.