I - Rules
(see JITD, p. 22; FAQ, p. 6-7)
Each time an enemy figure moves into a space adjacent to a figure with the Aura ability, it immediately suffers 1 wound that cannot be reduced by armor. The Aura ability inflicts no damage when the figure that possesses the ability moves adjacent to an enemy figure.
If a hero stays next to a monster with aura and doesn't move at all, he still suffers 1 wound per rank of the aura ability. To the question "What happens if you are on a lava space at the beginning of your turn and you don’t move?", the FAQ answers "If you begin your turn on a damaging effect, such as lava or a monster’s aura, and do not move off of it, you are damaged by it at the end of your turn."
Fly vs Aura
Figures with the Fly ability are affected by the spaces around an enemy with Aura but not the space where the enemy figure stands. The FAQ states that a flying monster passing through a hero that has Holy Aura, does not suffer a wound for the space it “shares” with the hero.
II - References
Heroes with the Aura ability: Shiver.
Skills granting the Aura ability: Holy Aura.
Feats granting the Aura ability: Sparks of Pain (1 turn only).