Nadis are pathways and channels of prana throughout the body, and there are about 72,000 nadis, and three major nadis. The major nadis are Ida, Pingala, and Shushumna. While they do not have a physical manifestation within the body, you will notice that the energy within the body, the prana, moves in certain pathways, which are the nadis.
Ida and Pingala represent the duality in all the Universe, and are traditionally personified by Shiva and Shakti. Shiva and Shakti are energies that move throughout the nadis, and are the same; not having one without the other. For more information on Shiva and Shakti, I recommend this site. Life would not exist without Ida and Pingala, the duality of existence. The Ida nadi relates to feminine attributes, and Pingala nadi to masculine attributes. These are not to be associated just with the sex of masculine and feminine, but with the attributes associated with each group.
Sushuma is the center in which the Ida and Pingala move through. It is attribute-less, neither feminine nor masculine. When the energies of Ida and Pingala move into Sushuma, the yogi enters Vairag. Vairag is essentially transparency, attribute-less with awareness. The yogi has pervading balance between the two nadis, and this balance permeates any outside disturbances or turmoil that may come from life. The yogi is untouchable by the outside forces. A great way to visualize this is with a crystal. The yogi, once entering Vairag, becomes like a crystal, reflecting the colors around it, but not becoming it. It reflects yellow, blue, green, but it is not either of the colors. No prejudice exists once the yogi is here in this balanced state. Only within this state can one explore the higher levels of consciousness.