If you'd like to know what's actually going on here, I recommend the book "The Black Hole War" by Leonard Susskind. I'll summarize as best I can - I'm a layman but I have a pretty keen interest in the subject.
What's at stake here is the physicists' concept of "information". Information, in physics, has several important attributes - for example, it cannot be transmitted faster than the speed of light, or c (quantum entanglement/teleportation does not violate this rule because it does not transmit information. In case you were wondering). The term c is probably a better choice than "speed of light" as c is the speed limit of ANYTHING in the universe, and this is of course the significance of a black hole - when you compress enough mass into a small enough space, you create a region where escape velocity exceeds c, and the boundary of that region is what we call the event horizon. A more important attribute of information, for this discussion anyway, is that it is indestructible, and it is conserved in all reactions - even if it would be impossible to do in any practical sense, for example, it is theoretically possible to take the ashes of a burned book (together, I suppose, with the smoke and heat released from the combustion), and "rewind" the burning process to get the original book back. Everything that happens in the universe is thought to be rewindable in this way, and if an exception were to be found, some major parts of quantum physics would fall completely apart.
Black holes are that exception.
Or at least, they were once thought to be. Stephen Hawking was the first one to point this fact out, and it's the source of his famous quote "not only does God play dice, sometimes he throws them where they cannot be seen".
The problem is entropy - you can think of every event in the universe (like our burning book) as following this equation:
Original State + Entropy -> Final State
And just like simple addition, physics expects the equation to work in the other direction, too.
Final State - Entropy -> Original State
But black holes don't seem to have any entropy! They were thought to be smooth, featureless, almost perfectly mathematical entities, possessing only mass, charge, and spin. (Another memorable quote from this period was "a black hole has no hair"). A book that falls into a black hole isn't even recoverable in theory, it is permanently lost, indistinguishable from every other piece of matter that's passed through the event horizon.
OK, so maybe the information isn't available to us anymore but it's still somewhere, you might think. Just trapped behind the event horizon, lost to us, maybe, but not destroyed. Turns out, no - Hawking made matters worse when he observed that black holes ought to emit radiation, and to decay as they do so - this is a weird one, but the explanation isn't too tough to understand... In quantum mechanics, even perfectly empty space is constantly bubbling with activity, as matched pairs of particles and anti-particles pop into existence for a brief period of time, then reconnect and annihilate each other. This is happening all the time, everywhere. But at the event horizon of a black hole, there's a possibility that the particle with the opposite charge of the black hole will be pulled in, and the other will be simultaneously repelled. Since opposites not only attract, they annihilate, that means the black hole is constantly losing some of its mass to these reactions, and releasing it in the form of particles with no connection, information-wise, to the matter that made up the hole itself (save charge and mass). It was bad enough when information was falling into the black hole and being trapped there, but to find out that it was also being permanently destroyed was a major crisis for quantum physics. The theory not only couldn't explain it, but major parts of it would have to be thrown out if it were true. And since we have, in fact, found evidence of Hawking radiation, quantum physics has a serious problem.
Has, or maybe had. "The Black Hole War" describes how at least part of the conundrum was resolved. A number of physicists (none with Hawking's PR department, sadly) developed a theory in which the event horizon was, itself, the black hole's entropy. If you've read something recently about the universe being a hologram, this is exactly the line of reasoning that's under discussion... The surprising result that all of the information that had fallen into the black hole might be preserved right at its perimeter lead to the even more surprising result that all information in the universe can be thought of as residing at *its* perimeter. (If you know what a nonogram, or Japanese Crossword is, it's an extremely helpful metaphor here). Hawking himself seems to have signed off on this theory, having paid off a $1 bet he made that the problem of black hole entropy would never be solved.
Which makes me wonder where this new theory of his is coming from... I'm not sure if he's just restating the work other people have done (wouldn't be the first time), or if there's some further difficulty he's trying to resolve that I'm not aware of. In any case, this doesn't mean anything like "there are no black holes" - there are, and there's likely one at the heart of every single galaxy, including our own. It just means they don't behave like the perfect geometrical fields of force predicted by relativity, but are rather stormy, complex, and, well, hairy things after all.