Exploding die
An exploding die is a term used when achieving certain results on a roll allows additional rolling to achieve more significant effects. For example, in new World of Darkness, rolling a 10 adds a success to the skill attempt in question and grants an extra roll of the d10 to the player, allowing more successes than usually possible to be achieved. In L5R, any tens rolled are rerolled and the new number added to the previous 10 to determine the result of the dice throw (if this is also a ten, the process repeats, allowing lucky players to achieve truly ridiculous results).
In the strategy/RPG game Mekton, rolling a 10 on the Location Damage chart to determine where a shot hits will upgrade it to a critical. Rolling another 10 will force the opposing player to save (and take 50% damage to the affected area) or die instantly if the shot breaches armour, while a 8 or 9 will cause a critical hit.