My rather pop-sci understanding is that when you start playing around with relativity math, trying various masses and densities you hit something rather worrisome. As you approach some great, but still possible, value the plot goes infinite, the singularity. This is bad for the theory because going asymptotic like that usually indicates a fundamental problem in the math. But relativity does so well everywhere else... What if it could? And thus the black hole was born.

The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.