A black hole is an area of space-time dimensions where gravity has won over mass. Black holes are the evolutionary end point of a relatively big star (by ‘big’ I mean a star whose mass 10 to 15 times the mass of the Sun). When a star that massive dies, or in other words, runs out of fuel and undergoes a supernova explosion, it leaves behind burnt-out stellar remnant. These relics would later collapse on themselves due to gravitational forces, creating what’s mathematically known as a singularity, that’s briefly, a point of zero volume and infinite density. To give you a better idea, if Earth were a black hole, the blue planet would be the size of a marble. For a really cool animation to introduce black holes, check this link from an award winning astronomy website.
|Black Holes are where God divided by zero.|
Keep in mind, that these black holes are not, contrary to popular belief, cosmic vacuum cleaners. For example, if the Sun were to be replaced by a black hole of equal mass, the Earth’s orbit would remain unchangeable.
The gravity of a black hole is so strong that its escape velocity exceeds the speed of light (quick definition of escape velocity: the lowest velocity that a body must have in order to escape the gravitational attraction of a particular object), since we don't know of anything that moves faster than the speed of light, then nothing can escape it, ergo the appellation "black hole".
For a quick classification of black holes:
The anatomy of a black hole consists of: (for a cool animation click here)