Shinigami Ranking is a system in which Shinigami are each given a rank to fit their statuses.
Shinigami are ranked from highest to lowest, with the lowest being the more superior. Despite there being far more than thirteen Shinigami, only thirteen ranks are actually given. It appears that higher stats contribute to a Shinigami's rank. The only Shinigami who does not have a rank is the King of Death himself.
While the system consists of numbers and all Shinigami have a different number, in the pilot series there appears to be a different ranking system, as one Shinigami says that because Ryuk is always losing his Death Note, he is "still a C-Rank Shinigami," suggesting that there is some alternative ranking system in which multiple Shinigami can be of the same rank.
Despite ranks being mentioned, it appears that ranks have no overall effect on anything in the Shinigami Realm. However, higher-ranking Shinigami tend to be closer to the King of Death.