The Schwarzschild radius is the distance from a massive object’s center at which its escape velocity equals the speed of light. Squeeze any amount of mass inside that radius and nothing, not even light, can travel fast enough to break free of its gravity again.
It is named after Karl Schwarzschild, who found this solution to Einstein’s equations within weeks of general relativity’s publication in 1915, while serving on the German front during the First World War. For an object with the mass of the sun, the Schwarzschild radius works out to about three kilometers.
Because it marks where escape becomes impossible, the Schwarzschild radius is also called the event horizon. Every object in the universe technically has one, but only the densest, like black holes, are ever actually compressed small enough to sit inside it. Read more from NASA’s Imagine the Universe.
The scale involved is easier to grasp with a comparison. Earth’s entire mass, if somehow compressed down to fit inside its own Schwarzschild radius, would need to be squeezed into a sphere only about nine millimeters across, roughly the size of a grape, for its gravity to become strong enough to trap light. No known natural process could ever compress the Earth that dramatically, which is exactly why planets never turn into black holes on their own. Only much more massive objects, typically stars many times heavier than the sun, ever reach the extraordinary densities needed to actually collapse inside their own Schwarzschild radius and form a real black hole, which is part of why black holes are relatively rare compared to the vast number of ordinary stars scattered across the galaxy.
Schwarzschild never lived to see how significant his solution would become, he died just a few months after publishing it, from an autoimmune disease contracted while serving on the Eastern Front. His radius remained a mostly theoretical curiosity for decades, since physicists at the time doubted anything could actually collapse small enough to reach it, until astronomical observations decades later proved otherwise.