Some TMNT stuff really isn't for little kids.
In the IDW continuity, the Gauntlet is an ancient Foot Clan ritual designed to end an irreconcilable feud between two warring clans. After a formal challenge is issued, two teams of four chosen champions are pitted against one another, and fight until all of the combatants on one side have been defeated. After this, the challenger and his opponent are to fight one another to the death, although any winning combatants from the first half may also contribute to the fight. The result of this is that the clans are no longer in conflict, and are honor-bound to observe the results of the Gauntlet.
In the Vengeance story arc, Splinter, in the name of his past life as Hamato Yoshi, issued a challenge to Oroku Saki (the Shredder), in order to finally remove the threat of the Foot Clan from his sons' lives. Shredder initially refused to accept the Gauntlet, but Kitsune convinced him to accept.
In the first part of the Gauntlet, the four Turtles representing Clan Hamato were pitted against Bebop, Rocksteady, Bludgeon and Koya representing Clan Foot. Despite the greater size and strength of their opponents, the Turtles were ultimately triumphant due to their superior use of teamwork and intelligence.
In the second part of the Gauntlet, the Turtles all fought the Shredder together, but were unable to overcome him due to their fatigue and his superior skill. After meditating upon his past experiences with the Shredder, Splinter finally fought his ancient enemy using his sons' weapons, mortally wounding him before beheading him, which completed the ritual combat with Clan Hamato as the victors.
Oroku Karai would later attempt to have the Gauntlet held in order to take leadership of the Foot taken away from Splinter. Splinter denied her request in order not to spill innocent blood, and Karai declared war on him and his loyalists in retaliation.