Remain Lights

Remain Lights, in ALfheim Online, are the leftover souls of killed players that remain in the place that they were killed in for about 600 seconds (10 minutes). During this time, the player can be revived on the spot with revive magic or items. If the player isn't revived before the timer expires, the Light vanishes and the player is returned to one's re-spawn point. Though dead players aren't able to move or take any action while they are dead, they can still hear and see what is going on around them.

Colors
The color of the Remain Light's flame is different for each race, based on their primary color:

Fairy Dance Arc
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 by Kirito in their duel, 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 resurrection time is 600 seconds (10 minutes), in the light novel, the timer actually last just for around a minute.
 * It's likely that 10 minutes was the penalty for dying 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.