The twist with its crisscross form represents the many paths of life and love and as such
 is regarded as the original eternity symbol. The single twist in particular shows the joining together of two people for eternity. Even though they sometimes move away from each other on their own journeys, they will always come together again sharing their lives and blending to become one. It tells how the strength of bond of friendship, loyalty and love will last forever.
The double and triple twists have a similar meaning but refer more to the joining of two peoples or cultures rather than individuals.
They also refer the the three baskets of knowledge.

Hei-Matau:

These very stylised fish hooks represent strength, prosperity,abundance, fertility and a great respect for the sea.
It also is said to provide good luck and safety when traveling over water so is often worn by travelers.
Hei-Matau are also symbols of power and authority which are held in great reverence by the Maori people.
They were used as a practical tool for fishing and were often decorated as a sign of respect for the creatures of the sea.
There are many styles of Hei-Matau from the true hook designs to the more ornamental styles which became treasured heirlooms for generations following.

Manaia:

The Manaia is an ancient mythical being with a birds head and a human form. It is said to be the messenger between the earthly world of mortals and the domain of the spirits illustrating the strong links the Maori people have with spirituality and the spirit world.
It is a holder of great spiritual energy and is a guardian against evil.
The Manaia can be seen blended into many Maori designs with subtle differences between tribes.

The Manaia is often depicted with the three fingers of birth, life and death. It can also be shown with a fourth finger representing the afterlife and describing the circle of life.

Toki:

This design represents the Toki or Adze ("adz" in American English) which was used to carve the great canoes and also to cut and work timber for the fortresses or Pahs in which the Maori lived. 
It was such an important tool in Maori life that it became regarded as a symbol of power, authority and good character. 
It is also the mark of the craftsman and artist.