Black holes are places where ordinary gravity has become so extreme that it overwhelms all other forces in the Universe. Once inside, nothing can escape a black hole's gravity — not even light. Black holes are the evolutionary endpoints of stars at least 10 to 15 times as massive as the Sun.
A black hole has something called an 'event horizon'. This is a spherical surface that marks the boundary of the black hole. You can pass in through the horizon, but you can't get back out. In fact, once you've crossed the horizon, you're doomed to move inexorably closer and closer to the 'singularity' at the center of the black hole. The horizon has some very strange geometrical properties. To an observer who is sitting still somewhere far away from the black hole, the horizon seems to be a nice, static, unmoving spherical surface. But once you get close to the horizon, you realize that it has a very large velocity. In fact, it is moving outward at the speed of light! That explains why it is easy to cross the horizon in the inward direction, but impossible to get back out. Since the horizon is moving out at the speed of light, in order to escape back across it, you would have to travel faster than light. You can't go faster than light, and so you can't escape from the black hole.
The nearest black hole is many lightyears away, so we don't have to worry about threats to the Earth.
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