The term Taekkyon (also spelled taekkyoen, or taekyon) is used to refer to what is believed to have been an ancient Korean martial art. Historical records regarding taekkyon, however, are scant. The first explicit written reference to taekkyon appears during the Joseon Dynasty. It is believed that there may have been multiple styles of taekkyon, with subak being an example of one style, but this is conjecture. Other authors believe that taekkyon may have been nothing more than a folk dance. Note that it is possible for both views to be correct: for example, over centuries a martial art could evolve to become a folk art, and in fact even in taekwondo today there is a tendency in Korea to combine martial arts with dance.
During the development of Traditional Taekwondo there was an effort by some of the Nine Kwans to ensure that traditional Korean influences were incorporated into the then-nascent martial art of taekwondo. Elements of taekkyon and Gwon Beop (to the extent that they were known) were intentionally incorporated into taekwondo, in part to distinguish it from Shotokan Karate. In fact, the name "taekwondo" was chosen in part as an allusion to taekkyon.
To the extent that taekkyon has survived at all today, it is characterized as a martial art by fluid, dance-like footwork. It utilizes a wide variety of kicks, fist and elbow strikes, pressure point attacks, throws, and grapples.
See Wikipedia (below) for additional detail.