Growing enchantment

Growing enchantments are enchantments that start out without the ability to do anything but "grow". A "growing" enchantment accumulates counters on it's controller's upkeep, building up to produce an effect proportional to the number of counters. While those in Urza's Saga all used verse counters and sacrificed themselves, the ones in Urza's Destiny were Auras and had more varied counter names and impacts.

Although other spells with a similar mechanic have appeared before or since, growing enchantments were a widespread theme in the Urza block. There are also two artifacts in Urza's Saga that behave this way: Barrin's Codex, which accumulates page counters, and Lotus Blossom, which accumulates petal counters. Powder Keg was released in the next set with a destructive effect.

Thirteen years later, Golden Urn and the Shrine cycle from New Phyrexia follow the same theme, though the Shrines have the bonus ability to gain counters when a spell of an appropriate color is cast.

Rulings

In a sense, these enchantments behave like delayed-effect sorceries. You cast one, then you wait. The more turns you wait before sacrificing it to get its effect, the bigger that effect will be.
Putting a counter on the enchantment when its upkeep trigger resolves is always optional.
The sacrifice ability's effect checks the enchantment's last existence on the battlefield to see how many counters were on it.