Anxilia is the name used to refer to a group of 'Living' or 'Sentient' Masks formed by the power of the Red Star's Lightning. They can communicate with the Toa using their inhabited mask through their thoughts, although not to the point of full on telepathy or 'mind exploration'.
Shape and Mentality
Anxilia are only truly 'seen' as beings by their host Toa, whom they can project their thoughts of their physical form unto. Most of the time, Anxilia have a form that their host Toa can also create with their powers, though this is not always the case. An Anxilia's physical form is humanoid, and can be male or female, which corresponds to how they think of themselves as.
Powers
Apart from 'thought communication' with their host Toa, Anxilia also receive the power of the Kanohi Mask that the Toa is using. The 'general guidelines' for their powers are that they can only operate it the same way the Toa might use it, and that the Kanohi is still powered by the Toa's energies. The Toa, however, cannot control how the Anxilia makes use of their powers. So usually they're friends with the Anxilia. Several examples include:
1. An Anxilia being able to heighten the Toa's physical and mental capability to its max with a Calix, while also being able to heighten his/her own mental capabilities while using more of the Toa's energy.
2. An Anxilia being able to use Telekinesis with the Matatu, while the Toa cannot control it.
3. An Anxilia making the Toa (And the mask) invisible with the Huna.
Formation
The exact process as to how Anxilia form is unknown, although it is known that Anxilia are usually formed when a being - already a Toa - is struck by Lightning from the red star, which reportedly contains Toa energy in it as well. One of the theories is that Anxilia are formed because the Toa energy, having nowhere to go while inside the body of a Toa (Due to it being Toa anyways) is focused on the mask, causing it to gain life. Several instances back this theory up: For example, Ketru, a Toa who wears an Anxilia, is much more mechanical than average. His mask is also different, much more organic than average.