Agni Kai

Agni Kai is the fire duel. It is done by members of the Fire Nation. The loser may die, but not always. The outcome affects th ehonor of both dulers. It seems like a popular way to resolve conflicts, and a source of entertainment for spectators.

Process
Fire Nation citizen A is arguing with Fire Nation citizen B. A chalenges B to Agni Kai. B accepts. They go to an arena to fight. They walk onto the arena floor with some sort of brown cloth around their necks. They assume a fighting stance and the cloths fall to the ground. Using various fire bending moves, one A and B fight until one, in this case B, falls to the ground or dies. The match is now over.

Other duels
Other, less oficial varsions of Agni Kai exist. One example is what Prince Zuko and the leutenant do in The Storm.

Meaning
In hindu Agni means fire, and Kai means meeting, so the name was not created by the producers of Avatar: The Last Airbender