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.
Nakomi appeared to Aviendha, apparently traveling alone and without food or water. Despite the strange circumstances, Aviendha offers her shade, sharing food and water with the woman. 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. Nakomi then leaves, promising to return momentarily, but then mysteriously vanishes.
Her words are most likely the vital catalyst that Aviendha requires in order to change the effects of Rhuidean's glass columns, allowing her to see the possible future of the Aiel. 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 major theories, in order of generally accepted likelihood of being correct.
1. "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.
2. "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.
3. "Nakomi's Soul is Brown" - 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.
4. "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