I.e. Elemental damage, such as a bonus fire damage, cold damage, ice damage etc. There are different abilities that can be associated with aura thusly:

White Aura: Turns a character white, giving them Ice elemental attack.

Yellow Aura: Turns a character yellow, giving them more Critical Hit
chance.

Green Aura: Turns a character green, giving them Poison status attack.

Black Aura: Turns a character black, giving them Death status attack.

Blue Aura: Turns a character blue, giving them Bolt elemental attack.

Orange Aura: Turns a character orange, giving them Soul elemental attack.

Red Aura: Turns a character red, giving them Fire elemental attack.

AFAIK only one status from the aura can be active. The auras appear from Level 1-7 in the order I listed above (i.e. level 1 gives white aura, level 2 gives yellow or white aura, level 3 green, yellow and white etc.)