According to Google, Stephen Hawking is the most famous physicist alive, and his most famous work is the black hole information paradox. If you know one thing about physics, therefore, that’s what you should know. Before Hawking, black holes weren’t paradoxical. Yes, if you throw a book into a black hole you can’t read it anymore. That’s because what has crossed a black hole’s event horizon can no longer be reached from the outside. The event horizon is a closed surface inside of which everything, even light, is trapped. So there’s no way information can get out of the black hole; the book’s gone. That’s unfortunate, but nothing a physicist sweats over. The information in the book might be out of sight, but there’s nothing paradoxical about that.
Then came Stephen Hawking. In 1974, he showed that black holes emit radiation and this radiation doesn’t carry information. It’s entirely random, except for the distribution of particles as a function of energy, which is a Planck spectrum with temperature inversely proportional to the black hole’s mass. If the black hole emits particles, it loses mass, shrinks, and gets hotter. After enough time and enough emission, the black hole will be entirely gone, with no return of the information you put into it. The black hole has evaporated; the book can no longer be inside. So, where did the information go?
You might shrug and say, “Well, it’s gone, so what? Don’t we lose information all the time?” No, we don’t. At least, not in principle. We lose information in practice all the time, yes. If you burn the book, you aren’t able any longer to read what’s inside. However, fundamentally, all the information about what constituted the book is still contained in the smoke and ashes.