Black holes are a good example of information destruction. Matter and energy fall into the gravity well, and eventually are reemited as Hawking radiation, but as far as current theories go, there's no way to reconstruct the information that made up the original matter or energy from that radiation.

Information isn't a "thing" but the relationship between, and exact quantum state of, things. Once that state is disrupted, the information is gone.

That's interesting. If the text had made it clear it was optional I definitely would have skipped it. Hopefully that will be easy to fix.