Trial by Stone is a ceremony used by the Skeksis to settle disputes, debates, and conflicts. Two competing Skeksis each get one attempt to break the ceremonial rock by striking it with a large sword-like blade. The Skeksis who is able to hack off the biggest chunk of the stone is declared the winner, and the loser is forced to forfeit his position in the Skeksis court.
According to The World of The Dark Crystal, the stone was created by the Skeksis in an attempt to create a dark crystal of their own, until they realized it would never match the original's power. The actions of the ceremony ceremoniously symbolize and mirror the shattering of the crystal.
In The Dark Crystal, after the death of Emperor SkekSo, SkekUng the Garthim-Master and SkekSil the Chamberlain participate in a Trial by Stone in a fierce rivalry for the throne. The Garthim-Master emerges triumphant by chopping off the entire top half of the stone, shocking the rest of the court and leading the Chamberlain to be banished from the castle.
Legends of the Dark Crystal shows that another contest is Trial by Fire.
In the Skeksis' original alien language (seen on the DVD releases' "original work print scenes" and in the film's novelization) the ritual of Trial by Stone is known as "Haakskeekah".