In general, the Kais are rulers of a particular area of the universe. The first level of Kais are in charge of their quadrant, there are 4 quadrants: South, North, East and West. The second level of Kais is the Grand Kai which is above the 4 quadrant Kais. Finally, the third level of Kais are the Kais of the Kais or the GODS of GODS.
East Kai- is the only female among the ruling Kai's and controls the East quadrant of the universe, which is known for it's speedy fighters.
West Kai- Short and chubby, West Kai controls the Universes West Quadrant, which is the home of many incredible warriors. Pikkon is his prize fighter.
King Kai (or North Kai)- Living in the 'Next Dimension,' King Kai is known throughout the universe as one of the greatest fighters and martial arts teachers (although his teaching methods are rather unorthodox). His house is on a tiny planet at the end of Snake Way. The small planet has ten times the gravity of Earth, and is thus an ideal training site. His companions include a goofy monkey named Bubbles and a grasshopper named Gregory. King Kai possesses a humorous, corny sense of humor (he's always telling jokes or puns) as well as great wisdom. Fortunately for our friends, he can communicate telepathically, giving them good advice and warnings in critical situations. Goku trained under King Kai and now wears his symbol. Yamcha, Chiaotzu, Tien, and Piccolo also train under King Kai when they are sent to the 'Next Dimension.' When Goku seeks King Kai in the 'Next Dimension,' King Kai begins his training by having Goku catch Bubbles - no easy task with an energetic monkey and a gravity ten times the force of earth's. Goku catches Bubbles after only three months. His next task is to hit Gregory the grasshopper with a hammer. Goku, impressively, performs this task in three weeks. Only after these tasks increasing Goku's strength and speed, does Kai begin the personal training of Goku. In the 118 days left before the Saiyan's return, Kai teaches Goku the 'Kaio-ken' and how to gather energy from the planet into one great fighting energy ball to form the Genki Dama or Spirit Bomb. Later King Kai takes on the training of Yamcha, Tien, Chiaotzu, and Piccolo using the same techniques that were successful with Goku.
North Kai- The Earth is in the North Quadrant of the universe or King Kai (description above).
South Kai- South Kai is the ruler over the South Quadrant of the universe. His quadrant has the reputation of being a peaceful area of space because all the fighters from this quadrant are comparatively weak.
Grand Kai- The Grand Kai rules over the four Kais. He is second only to Supreme Kai as the overseer of the entire universe. He is also the overseer of the Other World tournament. Grand Kai is reputed as the greatest fighter in the universe, but hes been out of training for centuries.
Supreme Kai- The Supreme Kai is the highest ruler remaining after Buu's elimination of the other Kais years ago. He becomes the Supreme Kai by default, ruling over Grand Kai and thus all life in the universe. He comes to Earth during the World Martial Arts Tournament to warn Goku about Babidi's plan to revive Buu and to prevent it from happening.
Elder Kai- was the ruling Kai, and most likely the Supreme Kai, 15 generations before the current supreme Kai. After his death, Elder Kai was trapped in the Z sword. When Gohan snapped the Z Sword in two while training, Elder Kai appeared and agreed to bring out Gohan's true powers.