A black hole is a region in space where gravity is so strong that nothing, not even light, can escape. While they cannot be seen directly black holes can be detected by the effect their immense gravity has on nearby objects.
Artist's concept of a black hole.
Black holes have such strong gravity because their mass (which is tens to millions times the mass of the Sun) is confined to an extremely small region. This is called the singularity, a region of infinite density and infinite smallness, that cannot be described by the normal laws of physics.
The boundary of a black hole is called the event horizon. It is an invisible boundary but once across it you are pulled in towards the black hole with no means of escape. Furthermore, nothing within the event horizon can be seen by the outside world. The radius of the event horizon (in kilometers) is equal to 3 times the mass of the black hole (in solar masses).
Inside the event horizon, gravity increases rapidly as you approach the singularity. The change in gravity is so strong, that say you were to cross the event horizon feet first, your feet, being closer to the singularity will be under more gravity than your head. You would be stretched length-ways and squeezed sideways to form a long thin string of spaghetti before being ripped completely apart!
And if that's not bizarre enough, black holes also change the pace of time. Our common sense drives us to believe that time is constant but time slows down when gravity is strong (as predicted by Einstein's Theory of General Relativity). Experiments comparing clocks at the surface of the Earth to clocks placed at the top of multi-storey buildings, in high-flying aircraft, and in space flights, have shown that the ground-level clocks that are closer to the Earth's centre of gravity, run a little bit slower.
If you were to watch someone cross a black hole's event horizon and they happened to be carrying a clock you (the observer) would see the clock's second hand slow to an almost stop. The ill-fated person would appear frozen in time, hovering near the event horizon.
But the person falling would have no such reprieve. And in fact, if they tried to slow down it would only make things worse. For time also slows when accelerating. So the best advice for a person falling into a black hole is not to try and stop! By braking (decelerating) time speeds up and you approach the singularity faster than if you did nothing. Isn't physics strange!
Black holes do not roam the Universe devouring everything in sight. If the Sun was to suddenly be replaced by a black hole with the same mass as the Sun the Earth would continue to orbit as if nothing had happened. We would, however, notice the distinct lack of heat and sunlight!