When something astonishes you, it shocks you or amazes you. It makes you stop and stare. It makes you think, "WOW." Or "WHOA." Or "WHAT?!" Or "REALLY?!"
Astonishing things can be good OR bad, but they're always surprising.
You'd be astonished if your dog suddenly spoke to you in English. You'd be astonished if your parents told you, "We're moving to a different country tomorrow." And if your friends teach you to play a new game, and you're extremely good at it right away, you'll astonish them.