If you are fascinated by the concept or imagery of black holes, even in the dramatic or fantastical sense that sci-fi media presents them but don't quite grasp 'what' they are or the scientific problems surrounding them are then please read on.
First, allow me to convey a more workable image of a black hole for you. Take a large, heavy bowling ball and put it at the center of your bed. Notice how the sheets and mattress sink in around the ball and warp the fabric around it. Farther away the warp is more subtle but closer in it becomes dramatically more visible. Now take a small marble or gumball and roll it across the bed in a path that doesn't intersect with the bowling ball. If you rolled it very lightly, the path the smaller ball takes spirals inward toward the larger ball until it meets. If you roll the smaller ball harder it might bend a little toward the bowling ball but ultimately continue across the bed.
What you just did was simulate pretty much gravity and space for objects in it. If that bowling ball was a sun and the marble a comet, pretty much the same thing would happen. Now imagine a bowling ball so heavy it sinks through the mattress and sheets leaving nothing but a void, a hole. You roll the small marble just like before and notice that if you don't roll it hard enough it just sinks into the void, and no matter how hard you roll it, if it crosses a definable boundary, the cliff of the hole in the mattress, the marble can't roll out.
That is what is happening around a black hole. So much mass in such a small area as warped space into a void that even the fastest things(traveling at the speed of light, the cosmic speed limit) can't get out once they have crossed the threshold, the event horizon.
Okay now that you can grasp whats going around a black hole, what exactly is happening inside of it. What state of matter and energy and space is reality past the event horizon? Is it all being crushed indefinitely into an ever smaller point with no limit? Is it 'bubbling out' into/through another expanding dimension filled with the matter-energy sucked inside? Something totally different?
Well to answer that question we need to apply a model of understanding. For the super massive scale of large objects like stars, galaxies, the context of gravity we use General Relativity. For the super small scale of small objects like photons, quarks, and the forces that play with them, like electromagnetism, strong/weak nuclear forces, etc, we use Quantum Mechanics.
Black Holes are both super massive, gravitationally immense but also indefinitely small inside the event horizon. So we can't have a workable, complete understanding of them unless we use both General Relativity and Quantum Mechanics. The problem is, attempting to apply both models results in nonsense. Mathematically anomalies, contradictions, and noise fill the interplay when this is attempted meaning that the models, while individually well refined and very verified in their respective context, when combined are simply an incomplete picture.
The problems are most notable when you examine space at the ultra small scale when gravity is incorporated. As you know from above, objects in space warp and bend space itself around them, this includes tiny particles themselves like quarks. However, the Quantum Mechanical model also makes these particles very fuzzy and violent. They exhibit odd characteristics like wave properties and their location and velocity can be indeterminable.
Well, what happens to space in the presence of this reality of particles? It becomes a roiling, chaotic foam, a horribly violent soup of space-time that pretty much makes any kind of modeling or useful information moot, you simply can't get anything useful or reasonable from space at this level and thus the core of the anomalies when you try to apply both Quantum Mechanics and General Relativity together and the reason why Black Holes are such a curious thing for science.
They are basically a huge red light to physicists that say "Hey, you think you can get away with dividing the universe into the small and large and think you could have a complete understanding of everything? Pffft."