As shybull said, Av mode normally chooses a shutter speed that will expose correctly under ambient light and then the flash fires to fill in the shadows.
Your shot, at a focal length of 115 mm, was taken at a shutter speed of 1/3 second. That's guaranteed to be blurry.
The answer? Don't use Av for flash unless fill flash is what you want.
You could use Tv at a higher shutter speed, up to 1/250. The higher your shutter speed, the less illumination you'll see from ambient light. At 1/250 all the light will be from the flash.
For most flash use, M is the best choice. If you want flash illumination only, choose 1/250 and f/8 or so. If you want some fill, use a slower shutter speed and larger aperture.
The flash exposure will be correct no matter what aperture and shutter speed you select (within reason) because the 580EX will adjust its output automatically.
-js