The Akatsuki is an organization that consists of rogue shinobi who have abandoned their respective villages, and work as mercenaries around the world. Interestingly, each of them had their own objective for joining the organization. Nagato Uzumaki was the leader of Akatsuki.
The Akatsuki has a total of ten members. They all work in pairs and are usually paired in a way that their combat skills compliment each other.
Nagato Uzumaki was the leader of Akatsuki. He gave each of the Akatsuki members rings to be worn on a specific finger. All the rings had Japanese Kanji symbols that are related to Chinese Mythology. Each member is supposed to stand on a specific finger of the Gedo Statue, which is the same finger as the one on which they wear the ring.
The rings help the members in sealing tailed beasts into the Gedo statue. The rings are very important and irreplaceable. The different Kanji on their ring would appear to indicate that the sealing was taking place. The ring was made by Nagato, and due to transferring the chakra between the rings, it also acts as a communication device between the members.
This also allows him to keep tabs on all the members. This ring helped the members to project themselves during meetings.
Itachi wears a red ring with the Japanese Kanji 朱 (Shu) which means ‘Crimson’ or ‘Scarlet’. The ring has to be worn on the right ring finger.
Sasori wears a purple colored ring with the Japanese Kanji 玉 (Gyoki) which translates to ‘Jewel’. Sasori has to wear the ring on his left thumb. After his death, when Zetsu and Tobi go to find his ring, Tobi then replaces Sasori.
Tobi wears the same purple colored ring with the Japanese Kanji 玉 (Gyoki) which translates to ‘Jewel’. After Tobi takes over the Akatsuki after Pain's death and after killing Konan, he discards his ring along with his cloak.
Kisame wears a yellow ring with Japanese Kanji 南 (Nan) which means ‘South’. Kisame has to wear his ring on his left ring finger.
Konan wears a ring that is white in color and has the Japanese Kanji 白 (Byaku) which means ‘White’. She has to wear the ring on her right middle finger.
Pain wears a blue or yellow ring which has the Japanese Kanji 零 (Rei) which means ‘Zero’. He has to wear the ring on his right thumb. His ring isn't related to a Chinese God like the other rings.
Orochimaru wears a red color ring which has the Japanese Kanji 空 (Ku) which means ‘Sky’ or ‘Void’. Orochimaru wore his ring on his left little finger. After he left the Akatsuki, he took his ring with him, and that is why he could never be replaced.
Deidara wore a ring that was blue in color with the Japanese Kanji 青 (Sho) which translates to ‘Blue’. Deidara used to wear his ring on his right index finger. After Deidara loses his arm with the ring during his fight with Sasuke, he was way more concerned about recovering the ring rather than his arm itself.
Hidan wears a ring that is orange in color with the Japanese Kanji 三 (San) which means ‘Three’. Hidan wears his ring on his left index finger.
Zetsu's ring is yellow or red in color with the Japanese Kanji 亥 (Gai) which means ‘Boar’. Zetsu has to wear his ring on his little right finger.
Kakuzu wears a ring that is blue in color and has the Japanese Kanji 北 (Hoku) which means ‘North’. Kakuzu must wear his ring on his left middle finger.
A. The Akatsuki has ten rings for each of its ten members.
A. Each of the Akatsuki has their own unique ring. No two members wear the ring on the same finger.