In our normal lives, we have total freedom of movement in space. You can walk left, right, forward, or backward. However, you are utterly enslaved by time. You must move forward into the future, second by second. You cannot stop the flow of time, nor can you reverse it.
Inside a black hole, this logic inverts.
Once inside the horizon, the radial direction (the path toward the center) becomes your new time. Moving toward the center is no longer a choice of destination; it is an inevitability, just as moving toward "tomorrow" is inevitable for you right now. Consequently, the singularity—the infinitely dense point at the center—is no longer a physical location sitting in the middle of a dark room. It becomes a future event.
Trying to stop yourself from hitting the singularity is as impossible as trying to stop next Tuesday from happening.
The Waterfall of Space
To understand why this happens, imagine space itself as a river flowing toward a waterfall. Far away from the edge, the current is slow, and you can swim upstream (away from the black hole) faster than the current pulls you in.
As you get closer, the current speeds up. The event horizon is the precise line where the river flows at exactly the speed of light. Since nothing can swim faster than light, once you cross that line, you are swept over the edge. Inside the horizon, space is falling toward the center faster than light. You could shine a flashlight directly backward, away from the center, and the beam of light would still travel backward into the singularity, carried by the rushing current of space.
Spaghettification
What you physically feel depends entirely on the size of the black hole.
If you fall into a small, stellar-mass black hole (one created by a dying sun), you won't live long enough to worry about geometry. The gravity at your feet would be so much stronger than the gravity at your head that you would be stretched into a long, thin strand of biological matter. Physicists call this "spaghettification." You would be ripped apart long before you even reached the event horizon.
However, if you fall into a supermassive black hole—like the one at the center of our galaxy or the monster in the movie Interstellar—the ride is surprisingly gentle. The event horizon is so far from the center that the difference in gravity across your body is negligible. You would cross the horizon without feeling a bump, perhaps not even realizing you had sealed your doom.
The View from the Inside
If you survived the crossing, the view would be mind-bending.
As you look back toward the universe you left behind, the light from the outside world would be compressed. Due to extreme gravitational blueshifting, the light from the stars behind you would shift toward the violet end of the spectrum and amplify in intensity. You would essentially see the entire future history of the universe playing out in fast-forward, concentrated into a blindingly bright disk of high-energy radiation behind you.
The End of Physics
Ultimately, you reach the singularity.
According to General Relativity, this is a point of infinite density and zero volume. It is a place where the curvature of spacetime becomes infinite. But in reality, "infinite" is just nature's way of telling us our math is broken.
At this scale, General Relativity (the physics of the huge) crashes headlong into Quantum Mechanics (the physics of the tiny). Nobody knows exactly what happens here. Some theories suggest you enter a wormhole; others suggest you are incinerated by a "firewall" of energy; most agree you simply cease to exist as biological matter, your mass added to the black hole's total, your personal timeline abruptly terminated at the end of time itself.