The Void, aka The Flame and the Void, aka The Oneness, aka Ko'di are different terms for a state of nothingness, a concentration or meditation technique used in combat arts throughout the cultures and Ages of the Wheel of Time universe. The mind is completely cleared from fears and emotions leaving the individual in a hyperaware state of consciousness to be able to focus exclusively on the desired task.
Blademasters enter the Void in order to achieve perfection in performing sword forms. Archers use the Void to aim without distraction. Channellers use the Void as a preparation to seize saidin, or in case of females they "open themselves to embrace the source".
"The Flame and the Void" refers to the visualization of a single flame of a candle into which the person could throw all their emotions, fears and obstacles which block them from performing. All concerns, thoughts, even the concerns of life and death - can be learned to be fed into the flame. This allows the user to perceive reality cleared from everything distracting. Sometimes other external focusing device is used.
Another technique is to imagine to become one with their weapon and one with their target or opponent, removing obstacles of rational thoughts and emotions such as the opponent is stronger or more advanced in combat, and such.
Danger in use
Being in the state of nothingness numbs the physical senses of the body of the performer. Cold or heat of the surrounding environment, pain of the injury, tiredness of the body, sourness of muscles are only observed from a distance as the subject would be someone else's body. One can simply bleed out, freeze or burn to death and watch their own dying emotionless from the Void.
Rand al'Thor first learned the Flame and the Void technique from his father, Tam al'Thor.  While in the Void, Rand excelled in archery, and he later learned to advance it from Lan Mandragoran while performing sword forms. When Rand starts involuntarily channel, he discovers The True Source as an uneasy glow flickering in the Void , so he tries to avoid the use of the technique, but he quickly discovers when fighting Turak in Falme that he is much less effective in combat without it. 
Malkieri call the technique ko'di. The word remained in their culture from the Old Tongue. Lan Mandragoran uses the technique to settle his mind during battle. While teaching the Emond's Fielders to use their weapons, he was very surprised to find out that Rand, a farmboy, knew the technique already. Lan also mentions that it is not exclusive to blademasters.
Throughout the books several people are mentioned using some form of the technique, including Galadedrid Damodred, and Gawyn Trakand who both became blademasters by killing another one. Galad killed Eamon Valda, Lord Captain Commander of the Children of the Light.  Gawyn killed Hammar, a Warder and blademaster, Master of Arms of the Tower Guard at the White Tower, when Siuan Sanche was deposed.
Lanfear call it The Oneness, which is most probably be the term from the Age of Legends. She encourages Rand to spend as much time in it as he can. "To learn the full use of it, it is best to wrap it around you continuously, to dwell in it at all times." 
Some martial artists, such as those training in Japanese Zen archery, use this state to allow the arrow to fly to its target at the most opportune time. Another example involves the Hindu hero, Arjuna, central to the Bhagavad Gita. Arjuna was able to hit a target with his arrow because he was able to precisely see a tiny target during the chaotic flow of battle. Many books and scrolls have been written on this subject, such as Issai Chozanshi's The Tengu's Sermon on the Martial Arts or a modern example, Peter Ralston's Cheng Hsin: The Principles of Effortless Power.
It should be noted that there are several paths to mindfulness. "The Flame and the Void" can be classified as a one-point meditation. In other one-point meditations, "The Flame" would be substituted for the breath or the tip of the nose. The concentration on doing exactly nothing is another, called wuxin in Chinese (mushin in Japanese). For more information on the practice of mindfulness, a good place to start is the book, Mindfulness in Plain English.