Who is Logain from Lord of Chaos and what is their importance?

Logain was once a False Dragon but is now cut off from magic. Most people cut off from magic simply lose the will to live and die, but Logain has hung on, likely for a chance at vengeance. When Nynaeve accidentally discovers how to heal Logain, however, he is reconnected to the power, though with less potential than he had before. At the end of the novel, Egwene lets him to escape.