Remain Lights

Remain Lights, in ALfheim Online, are the leftover souls that remain in the place they were killed for about 600 seconds for a player to revive after being killed, before the light vanishes and returns to their respective cities. While dead players can still hear and see what is going on around them. The color of the Remain Lights flame is different for each race, based on their primary color:

ALfheim Online
After Kirito skewers two Salamanders, they go up in flames, which are the Remain Lights. Their souls, after disappearing, go back to their city, where they restart their journey.

They are also present when General Eugene is killed, and later revived by Sakuya.

When Kirito attempts to clear the Grand Quest to climb the Yggdrasil, the World Tree, he is defeated by an onslaught of Guardian Archers. At this point, his Remain Light can be seen for the first time.

Trivia

 * Although in the anime it's stated that the ressurection time is 600 seconds (10 minutes), in the light novel, the timer actually last just for around a minute.
 * It's likely 10 minutes was the penalty for dieing to the main boss. This is probably the case, seeing how in both cases where Kirito wiped out the groups of Salamanders, their Remain Lights vanished rather quickly.