Dan-gun refers to Dan-gun Wanggom, the mythological figure who is said to have founded the nation of Gojoson in 2333 B.C.E.
Gojoson was located in what is now north-east China and Korea, and is considered by the Korean people to be the first Korean state, thus Dan-gun is viewed as the legendary founder of Korea.
The Legend of Dan-gun is a very famous legend in Korea, and is known by all Korean people. You can read English translations of the story online, including on Wikipedia.
The hangeul for Dan-gun is 단군.
Why not buy a Dan-gun poster?
Make learning the meanings of the patterns more fun with this poster about the historical figure of Dan-gun.
If you're a Taekwondo instructor, this would be an excellent poster to put up on the wall of your dojang to help students learn the meaning of the patterns. Or you could just put it on your wall at home!