Compassion is a close second, but ultimately the Avatar is a symbol of hope. He brings hope, he hopes for the world, that people's better nature will shine through. On the ship, it's hope that keeps him going while he holds back the nightmares. Hope that the others will survive, that his efforts won't be in vain. Hope that he'll see Katara again, in person, but if he doesn't, hope that the girl he loves just gets to live and be happy because of what he's doing.

Aang hopes. Aang inspires others to hope.

And because of this, Aang can change the world.