This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The Great Balance of Kaminar, Great Balance in short, was the central, organizing truth in the Kelpien way of life. It was forced upon them by the other species on their planet, the Ba'ul. (DIS: "An Obol for Charon", "The Sound of Thunder")
According to the Ba'ul, who appeared to have instituted the great balance to protect themselves from evolved Kelpien predation, the Great Balance was the only way to ensure these Kelpiens did not destroy everything in their path (DIS: "The Sound of Thunder")
Kelpien existence was oriented toward death and the role the Ba'ul played in it. Kelpien priests taught that the Ba'ul were the keepers of the balance, which if upset would devestate the fragile ecosystem of their planet. The priests explained that when a Kelpien reached vahar'ai, this meant that the Watchful Eye (a nickname for the Ba'ul) had chosen them to maintain the balance. They were then expected to offer their lives to sustain the Ba'ul, thus allowing their peers to live in peace and comfort. This was refered to as them joining the great balance. When the Ba'ul took a Kelpien, the pain of vahar'ai was said to stop, thus preserving the balance. (ST: "The Brightest Star"; DIS: "The Sound of Thunder", "An Obol for Charon")
During the 23rd century, an enquiring Kelpien called Saru engaged in a discussion with his father, a priest called Aradar. When he started asking critical questions about this state of affairs, Aradar reacted angrily and proclaimed that the balance must not be upset. (ST: "The Brightest Star")
Saru eventually joined Starfleet, where he became the first Kelpien in over two thousand years to pass vahar'ai. Shortly thereafter, a red burst lured his ship, USS Discovery, to his home planet, where they forced the Kelpien population of Kaminar to undergo vahar'ai, so that they could forge a new, true balance, which would protect everyone. Starfleet offered to help negotiate that balance. (DIS: "An Obol for Charon", "The Sound of Thunder")
A pre-meal prayer led by Aradar went: "We thank the Great Balance for replenishing the gift of light, and warmth, and for this food." This prayer was accompanied with a hand-gesture. (ST: "The Brightest Star")