Goju Kyokai is fairly young in it's development however its roots are deep in traditional Asian martial arts. The primary art to influence Goju Kyokai is Goju Ryu. This influence can especially be seen in the kata. Sanchin, Saifa, Seiyunchin and other traditional kata forms are an integral part of training.

Translation

Literally "Goju Kyokai Karate Do" can be broken down into the following:

Go (剛) - hard, strong

ju (柔) - gentle, soft

Kyo (協)- combined, cooperation

kai (会) - meeting, join 

Kara (空) - empty, void

te (手) - hand

do (道) - way, path, road

"Goju" becomes a single entity/word incorporating both hard and soft aspects (yin and yang). "Kyokai" is the joining and combination of the "goju" aspects.
"Karate-do" is the 'way' or practice of 'empty hand' or also the lack of weapons other than the human body. Bringing it together Goju Kyokai Karate-Do is a style of karate that brings together hard and soft features (technique, movement, thought etc) in the practice of the martial art and development of the individual.