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Why do black holes have such enormous gravity?

Short answer

It's not the mass that makes the difference, but the density. From far away, a black hole pulls with the same force as a star of equal mass. But because all that mass fits into a tiny space and no surface blocks the way inward, you can get very close to it: at the event horizon, not even light escapes.

Why do black holes have such enormous gravity?
Black hole - Messier 87Event Horizon Telescope (CC BY), vía commons

Same mass, shorter distance

If the Sun were replaced by a black hole of the same mass, Earth would remain undisturbed in its orbit; only the light would be missing. Attraction depends on mass and decreases with the square of distance, and a black hole changes none of that. Gravity only becomes enormous very close to the mass, and that is precisely where a black hole lets you get: it has no surface that blocks the path inward. In a star, the approach ends at the glowing gas envelope, far from the center.

The event horizon as a limit

Escape velocity increases the closer you are to the center. Where it reaches the speed of light lies the event horizon: beyond it, every path leads inward, including light's. The radius of that horizon grows in proportion to the mass. In a black hole formed from a spent star it is the size of a city, which is why tidal forces would tear apart any body just before reaching it. In the very massive specimens, the horizon lies so far out that the initial crossing would be quite unspectacular.

Two measured examples

At the center of the Milky Way lies Sagittarius A*, with about four million solar masses, at a distance of around 27,000 light-years; its mass was deduced from the orbits of the stars surrounding it. In the galaxy M87 there is a heavyweight of 6.5 billion solar masses at a distance of 55 million light-years. The Event Horizon Telescope has captured images of both. What is seen is never the object itself, but the luminous ring of matter and radiation that gravity bends around the dark shadow.