I needed this cute video to tell me what the heck conker is:
https://www.youtube.com/watch?v=cLGuZZraIqg
You and your opponent each attach a chestnut to a shoestring. You try to destroy your opponent's stringed chestnut by swinging your own stringed chestnut at it. The video explains different ways to cheat, such as coating the chestnut with nail varnish.