Countdown dice are polyhedral dice that are designed for the use of tracking health, levels, or other game attributes. They are a subset of counters, and are subtly different from regular dice.
Regular dice, sometimes referred to as random dice to distinguish the two types, are balanced so that adding any two opposing sides will result in the same number. For example, a regular six-sided die has the 1 opposite the 6, the 2 opposite the 5, and so on, so that adding two opposing sides will always result in a seven. On dice with higher numbers of sides, the sides are also arranged so that high (or low) numbers do not group together on the die -- making it slightly harder to intentionally roll the die with a useful side facing up.
Countdown die are most often d20s, but unlike random d20s, the countdown die will arrange the numbers so that you can always easily find the next number in sequence - 1 will be next to 2, 2 next to 3, and so on.
Countdown dice are generally not used for rolling, because one could theoretically cheat with them -- for example, if one rolled it with spin rather than tumble, one might be able to strongly influence their roll towards one hemisphere of the die, e.g., the side with the higher numbers. Also, if you are dealing with a loaded die, it is much more effective to weight a die that has all the the high numbers on one side of the die than if the numbers are more evenly distributed.
These dice are frequently used in Magic: The Gathering; in that game they are usually called Spindown LifeCounters or spindown dice.