What if I need to ship something breakable?

Whenever I take something to the post office to ship, they always ask if the package contains a list of things, one of which is breakables. I have never shipped anything breakable before, so what happens when I say yes?

It's a coffee mug and I have it packed really well. Multiple layers of bubble wrap and the bigger, air filled bag things to fill up any extra space, so it's not moving around.

I just don't want to run into any issues trying to ship this.