What comet gives firebenders tremendous power in the series finale?

The comet that gives firebenders tremendous power in the series finale is Sozin's Comet.

In Avatar: The Last Airbender, the comet periodically passes close enough to the planet to dramatically amplify firebending. Fire Lord Sozin used its power a century before the main story to launch the attack that destroyed the Air Nomads, beginning the Hundred Year War. Its return becomes the deadline driving the finale's conflict.

The comet is named after Sozin, the Fire Lord who first exploited its fire-enhancing effect for military conquest. During the finale, Fire Lord Ozai plans to use the same power to burn large portions of the Earth Kingdom. Zuko warns Aang and the others about the plan, making the comet central to the story even before it appears.

A common mix-up is confusing Sozin's Comet with the names of Fire Nation rulers connected to the story. Azulon and Ozai are characters, while Roku is a former Avatar; none of them names the celestial event. The comet's power enhances firebending generally, although Ozai's campaign gives the phenomenon its most terrifying role.