CN stands for Code Name while BLUE represents each member: ‘Burning’ - Lee Jong Hyun, ‘Lovely’ - Kang Min Hyuk, ‘Untouchable’ - Lee Jung Shin, and ‘Emotional’ - Jung Yong Hwa.
The band actually had its roots in Japan where they began in the indie scene in 2009 and released Now or Never and Bluetory. They finally got signed and debuted in Korea in 2010.
Here is Arirang's coverage of the group's official debut showcase in 2010:
In the last quarter of 2011, they returned to debut in Japan. By Feb 2012, their single Where You Are topped the Oricon charts.
Here's a video of the CNBlue's live performance in one of Korea's award shows:
Best about this group are their live performances not for their dances but for their chops in rocking the venue: