Basically a game where you take a ripe horse chestnut seed (known as a conker) and try to conk (smash) one held by another person. Usually the conkers dangle from a string, or shoelace or similar, and are held up by one person whilst another person similarly equipped tried to smash their opponents conker by striking it with their conker.
Individual conkers grew in stature with each successful survival of a game... oners... tenners...thirtyniners etc... The strength (and thus the life span) of the conker was often enhanced by arcane methods such as soaking in vinegar overnight or baking in an oven (remembering to bore the hole for the string first).