Kakyuu is the "First Order Imperial Princess of the Red Cercis Kingdom of the planet Kinmoku." It's rather unclear to me whether Kinmoku is the name of the planet or the name of the star; it's referred to as "Kinmoku-sei" which could go either way. I prefer to think of it as Kinmoku planet, which goes around Kinmoku Star.
Directly translated, "Kakyuu" means "Fireball." Her planet's name is a pun; it's written as "the planet Kinmoku," but the word "kimokusei" actually means "Fragrant Olive." (It's a sort of flower often used in perfume.) When Kakyuu first appears, the scent of fragrant olives is noted. Kakyuu and the three Starlights are the guardian senshi of the Kinmoku star system.
When Galaxia attacked the Kinmoku star system, Kakyuu and the Starlights fought her but were defeated. It is implied that Kakyuu's lover was killed by Galaxia right before her eyes. Weakened but not destroyed, Kakyuu and the Starlights fled to Earth.
Apparently, they got separated along the way. The Starlights arrived in a group, and posed as the male singing group the Three Lights on Earth. They hoped that the sound of their singing voices would bring Kakyuu.
Kakyuu, meanwhile, had been recuperating inside a sort of chalice. The chalice was guarded by the not-inconsiderable abilities of Chibi-chibi. When she was recovered, she emerged from the chalice to join her fellow senshi and explain the menace of Galaxia to Sailormoon.
Kakyuu is very close to the Starlights; more than just being their princess, she is their friend. They respect her greatly, and she loves them deeply in return. She was almost inconsolable when they were killed.