On the Na'vi, it is similar in appearance to long braided human hair, but is in fact an extension of the nervous system. It may look like that because the Na'vi braid it or because they have evolved the normally separate neural whip (as the structure is called on animals) pieces, as on most all over animals, into one. It is used to form tsaheylu, a connection with other living things, like other animals that possess a neural whip or antennae (such as the direhorse and mountain banshee) and plants such as the Tree of Souls. The Na'vi developed the queue harness for banshees, to hold them out of the way whilst riding.
This queue looks like a long braid, with many little pink, hairy, worm-like neural tendrils on the end. Animals have a different type, which is encased in a flap of skin at the end, where it has a wide structure that may serve to protect the tendrils, as well as allow a Na'vi to make tsaheylu more easily. The Na'vi use this organ to establish a neural-level connection to nearly any part of the Pandoran ecosystem. This connection is total, so both partners are in full control of the connected beings. The connection can serve many purposes, but is mostly used to enable a Na'vi rider to command his or her mount with his or her mind and with apparent little effort, and without use of their hands, which frees those up to use a weapon. This also enables her/him to use the mount's sensory organs. This also means that a Na'vi rider feels the pain when the connected animal is being hurt. In the case of communication with plant life, the vast network of connected nodes (plants) serves as a biological memory for Na'vi ancestors. Na'vi couples may also connect queues while mating, though this is purely to create an emotional bond and does not in itself lead to procreation.
The bonding of queues, tsaheylu, with a mountain banshee is a rite of passage that all young Na'vi hunters of the Omaticaya clan must pass. It is known as Iknimaya. The bond created between rider and animal lasts for a lifetime after the first flight has occurred.
The queues start at the top back of the Na'vi skull, but on an avatar it is located at the base of the skull.
Dr. Augustine mentions to Jake that playing with his queue could make him go blind. If that is true or not is unknown, though it is likely a reference to the once widely-purported human belief that masturbation causes blindness. The reference implies that a Na'vi's queue is considered an intimate area of the body.