Nakomi is a mysterious old-looking woman, appearing in the Tower of Midnight when Aviendha Travels to the Waste for her second path into Rhuidean and camps nearby for the night. Nakomi looks like an Aiel and Aviendha could not sense the ability of Channeling in her.  
Nakomi is middle aged with furrowed skin and graying hair. In her encounter with Aviendha, she is wearing the normal garb of an average female Aiel: a dark skirt, a tan blouse and shawl, and a kerchief on her hair. She wasn't carrying any weapons. She did not wear the clothing of a Wise One, but "there was something about her..." so Aviendha felt.
Nakomi was traveling alone (which was not unusual) carrying a pack but asking water from Aviendha. Despite the strange circumstances, Aviendha offers her shade and share her food and water with the woman. Nakomi pulls small branches for the fire from her pack, tea leaves, a teapot, several deepearth roots, and a small ceramic baking box. At a certain time Aviendha realizes that now there are coals on the fire, and she does not understand where they came from. Nakomi takes the roots from the box when Aviedha is sure they are not done, and yet they smelled and tasted wonderful. Nakomi pulled seasoning from her pack and also a pair of thin plates.
During the baking Nakomi shares contemplative insight, questioning the future of the Aiel once the Last Battle is over and the Aiel have fulfilled the purpose of their existence.
When Aviendha asks Nakomi about her sept, her answer is:
Right after they start to eat, Nakomi leaves to "see to nature" but she never returns. Aviendha finishes the meal and being worried goes to search for her but finds not even a trace of her. When she returns to her camp she sees that the plates and Nakomi's pack are also gone. She waits some more but the woman does not return. She goes to sleep being troubled.
Nakomi's words are most likely the vital catalyst that makes Aviendha try to do something with the glass columns ter'angreal in Rhuidean. (Perhaps Nakomi is even responsible for the recent changes in the effects of the columns, though this is just speculation.)
Who exactly Nakomi is is uncertain, although it is likely no coincidence that she appeared before Aviendha to deliver her words to her. 
Nakomi may have appeared a second time, as a mysterious, gray-haired woman in Aiel garb speaks to Rand as he exits Shayol Ghul.
Due to Nakomi's mysteriousness, understanding her exact nature is impossible, however, there are many theories. The following are the popular major theories, in alphabetical order.
An Agent of the Creator
This theory suggests that Nakomi is sent by the Creator to subtly help guide Aviendha to prevent the future she sees in the glass columns. This theory may be supported by the fact that food she prepares is the best Aviendha ever tasted, an effect very similar to that of Rand once he achieves balance.
Bubble of Good
This theory's logic is "If there is a bubble of evil, why can't there be a bubble of good?" It is similar to the "Agent of the Creator" theory, only this theory suggests that the event is a bit more random, rather than a premeditated action performed by the Creator.
This theory is about the mysterious Jenn Aiel who stayed loyal to Aes Sedai, built Rhuidean and the ter'angreal in it to make sure that Aiel live to serve their purpose in the Last Battle. Nakomi could be able to channel and hide her ability so Aviendha would not be able to sense it. Nakomi - as a One Power user - can be many hundreds of years old, just as many women in the Kin. So she would be able to make sure things are going to the right way including the very end when Rand gets back his life as an almost ordinary person in someone else's body, unrecognizable so he can live his life after he successfully fulfilled his role as the Dragon Reborn.
This theory revolves around the idea that Nakomi is Verin Mathwin, whether in real life or in Tel'aran'rhiod. Nakomi's knowledge she displays is very similar to what Verin learned in The Great Hunt in her conversation with Urien. The idea that this conversation could have been in Tel'aran'rhiod sprouts from the idea that you can pull someone from their dreams to the world of dreams. The Wise Ones explained this concept to Nynaeve al'Meara, answering a question she asked. They described it as "evil". This theory comes with some flaws. First of all, it is unclear whether Verin was alive when Nakomi appeared due to to the timeline discrepancies between The Gathering Storm and Towers of Midnight. The idea that Verin spoke to Aviendha out of the world of dreams is completely out of the question because there would be no way for her to perform the supernatural acts Nakomi did. As for the idea Verin pulled Aviendha into the World of Dreams, the possibility that Aviendha fell asleep without recognizing it is slim. In addition, there is no evidence that Verin can even enter the World of Dreams, let alone know how to pull someone out of their dreams.
Wise One's Advice
This theory is that the one Wise Ones that mentored Aviendha pulled her out of her dream and had their conversation. This theory is similar to the "Nakomi's Soul is Brown" theory and suffers some of the same flaws. Aviendha would have to have fallen asleep without noticing. The Wise Ones explaining how the concept was "evil" implied that they did not know how to perform it. Additionally, it doesn't seem likely any Wise One would have performed such an "evil" act unless they were a darkfriend. It doesn't make any sense that Nakomi would be anything of the Shadow since the only results of the things she discussed with Aviendha would be of benefit to the Light.
After A Memory of Light Brandon Sanderson would not answer three questions, one of them being the identity of Nakomi and her purpose in the series. http://www.tor.com/blogs/2013/01/brandon-sandersons-wheel-of-time-answers-from-torchat