What exactly is a black hole?

A black hole is a concentration of mass whose gravitational field is so strong that nothing can escape. Black holes are predicted by general relativity. General relativity (as well as most other metric theories of gravity) not only says that black holes can exist, but in fact predicts that they will be formed in nature whenever a sufficient amount of mass gets packed in a given region of space, through a process called gravitational collapse. For example, if you compressed the Sun to a radius of three kilometers, about four millionths of its present size, it would become a black hole. As the mass inside the given region of space increases, its gravity becomes stronger — or, in the language of relativity, the space around it becomes increasingly deformed. Eventually gravity gets so strong that nothing can escape; an event horizon is formed, and matter and energy must inevitably collapse to a density beyond the limits of known physics.
Balck holes are an end event rather than just something that happens randomly in space. It is theorized that most black holes are the collapse (or super nova) of a star. Seeing a black hole can be difficult; but they do exisit. As light is being pulled into the black hole, it will illuminate the horizon before succoming to it's invetable disappearance. Also, neighboring stars can also illuminate the black hole's horizon and make it visible in space.
Contrary to popular belief, black holes do not provide "worm holes" or bridges to make space travel faster. According to Einstein, worm holes can mathematically be proven; modern science has yet to find "worm hole."
sources: Nasa and Wikipedia!