Woody is a Sylph—basically a sky-delivery worker in Neo-Venezia. He's all about transporting packages and, more romantically, what he calls "people's treasured feelings." He genuinely loves the freedom of gliding through the sky and goes by Woody specifically because it feels less stuffy than his real name.
He's not the best navigator, though. In the manga especially, Woody's sense of direction is pretty rough, and he basically needs a map to function on the job. His childhood friend Akatsuki gets a lot of screen time with him—the two grew up playing outside together, with Al occasionally watching over them.
Content compiled by AnimeList.moe from publicly available sources.