event horizon
Imagine paddling a canoe up a river toward a waterfall. Far away, you can easily turn back. But there is a line on the water beyond which the current is faster than you can paddle — cross it, and no matter how hard you row, you are going over the falls. A black hole's event horizon is exactly that line, but for light itself. It is the boundary around a black hole inside which the pull is so strong that nothing, not even light moving at the cosmic speed limit, can ever escape back out.
The event horizon is not a solid surface or a wall — there is nothing physically there to touch. It is simply a location in space, a one-way membrane. An astronaut falling in would feel nothing special as they crossed it (for a large enough black hole), yet from that instant they are causally cut off from the outside universe forever; no signal they send can climb back out. Its size is set entirely by the black hole's mass: a 10-solar-mass black hole's horizon is about 30 km across, while the supermassive one at our galaxy's centre spans millions of kilometres.
The event horizon is what makes a black hole 'black' and what makes it a black hole at all — it is the defining feature, hiding the singularity within. It is also why 'nothing escapes a black hole' is true only of the region inside the horizon, not the space around it, where matter can orbit safely for ages. Remarkably, the first direct image of a black hole, captured in 2019, was really a picture of the glowing gas wrapped around an event horizon's silhouette — the shadow of the horizon itself.
In 2019 the Event Horizon Telescope released the first image of a black hole — a glowing orange ring around a dark centre. The darkness is the shadow of the event horizon; the ring is hot gas just outside it, bent into a circle by the black hole's gravity.
The 2019 black-hole image: a bright ring around the dark shadow of the event horizon.
The event horizon is a boundary in empty space, not a physical surface. For a big black hole you could cross it feeling nothing — yet from then on, escape is impossible even in principle.