Some stars are so massive that they collapse under their own weight. More specifically, the gravity the stars generate is so strong, the atoms they comprise are pulled together with such force that the stars actually shrink in size.
The problem is...this decreased size means that each atom's influence on every other atom increases exponentially. The more dense a star gets, the stronger its gravity becomes. As the star is shrinking without losing mass, its density continuously increases. So, the smaller the star gets, the smaller it becomes.
The star will eventually reach a point of zero size and infinite density, all of its mass packed into a single point of zero diameter. This is known as...
Singularities are an impossibility that is still somehow possible. They don't play by the rules. In fact, they crumple up the rulebook and throw it out. Or at least they would, if they could throw anything out. Which they can't, because their gravity is so strong that for an object to leave the space around it, the object would have to travel faster than the speed of light.
This means that light itself cannot escape or reflect off a singularity, making it look like a dark, void-like object drifting through space. These black-ish holey things draw matter in from trillions of miles away, consuming everything in their celestial neighborhood. The Milky Way has one of these greedy buggers at its center, keeping the billions of stars in the galaxy rotating around the central point of its tiny singularity.
The Black Hole
As the falloff of gravity is the inverse square of the distance from the object generating said gravity, every time you halve the distance between yourself and a black hole, you quadruple the amount of gravity you are affected by. Let's say you're floating a short distance away from a black hole, feet pointing toward it. As the gravity surrounding said black hole is absolutely insane, the mere distance between your feet and head is more than enough to expose your little piggies to a much greater amount of pull than your airy noggin. As you are pulled feet-first toward the galactic vacuum cleaner, the gravity difference between your head and feet becomes greater and greater until...
Every atom in your body are rent from each other as your feet are pulled faster and faster relative to your head. You can still be saved, of course, as long as you don't pass the event horizon.
The Event Horizon
This is the point of no return. The distance from a black hole where if you get any closer, it will suck you up like the thirsty bastard it is. Once you pass the event horizon, you're screwed. Let's face it, you're pretty screwed anyway, but if you traverse the horizon, you're extra screwed. Remember the thing about light not being able to leave the space around a singularity? This is that space. Though the singularity itself is infinitely small, this event horizon can be anywhere from several miles to many millions of miles wide.
What's inside the event horizon?
Why are you asking this question? Since light cannot leave the event horizon, there's no way to know what's inside it. For all we know, there could be a pink elephant.