Something astonishing is astounding, staggering, stupefying, amazing, or incredible. It's not something you see every day.
This is a pretty strong word. A dog shaking hands is not astonishing, but a dog calling 911 for its owner definitely is. Astonishing things are amazing; they blow your mind. When people first walked on the moon, that was astonishing. Miracles are astonishing. If you say, "Holy cow! I can't believe what I'm seeing," you're probably seeing something astonishing.
