A black hole begins to form when a star runs out of fuel and starts to cool off and so to contract. As it contracts, it becomes more and more dense, its gravitational field at the surface gets stronger and makes it more difficult for any thing, even a ray of light to escape from the star. Eventually, when a star has shrunk to a certain critical radius, the gravitational field at the surface becomes so strong that the light can no longer escape.
Since nothing can travel faster than light, nothing else also can escape, everything is dragged back by the attraction of the gravitational field. Such a region of space-time from which it is not possible to escape is called black hole.
Though a black hole is invisible, one would feel the force of its gravitational attraction. One such black hole is thought to exist in our own galaxy. The star called "Cygnus X-l" in our galaxy appears to consist of a black hole and a normal star, orbiting around each other.