Divinity counters, while having no inherent rules meaning, are consistently and exclusively used by an unnamed mechanic to grant permanents indestructible. Because they are not defined as doing so in the Comprehensive Rules, they only grant indestructible so long as a permanent with such an ability is on the battlefield.
Divinity counters first appeared on Champions of Kamigawa's myojin cycle: Myojin of Cleansing Fire, Myojin of Infinite Rage, Myojin of Life's Web, Myojin of Night's Reach, and Myojin of Seeing Winds. While the myojin were initially designed as having indestructible at all times, there was concern that they would be too powerful in reanimator decks. For that reason, they were changed to rely on divinity counters for indestructible, and only acquired divinity counters when cast from the hand. They are also used by That Which Was Taken from Betrayers of Kamigawa, which can add divinity counters and grant indestructible to any permanent.
They reappeared on Bant in Planechase and Kindred Boon in Commander 2017.