There are 24 standard patterns, one for each hour of the day. Each one has a meaning; elements are often symbolic of events in Korean history.
For example, in Hwa-Rang the name refers to the Hwa-Rang-Do group which existed in the Silla dynasty in the 7th century and which practiced Tae-Kyon, the precursor of Taekwon-Do; and the 29 steps refers to the 29th Infantry Division where GeneralChoi began to develop modern Taekwon-Do in the 20th century.
In Taekwon-Do, the highest rank is 9th dan; since there are 24 patterns, those testing for higher black belt ranks must learn more than one pattern.
The patterns which are listed beside the belt levels are the ones you will learn at that belt level.
You will need to successfully perform the patern(s) and other requirements listed to attain the next belt level.