The story
By surface analysis, conker + -s, although the game itself came before the modern meaning of conker as "horse chestnut". See conker for more details.
Etymology from Wiktionary, CC BY-SA 4.0.
conkers
Today it means: A game for two players in which the participants each have a horse-chestnut (known as a "conker") suspended from a length of string, and take turns to strike their opponent's conker with their own with the object of destroying the opponent's conker before their own is destroyed. Full definition →