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A black hole is a region of space from which nothing, including light, can escape. It is the result of the deformation of spacetime caused by a very compact mass. Around a black hole there is an undetectable surface which marks the point of no return, called an event horizon. It is called black because it absorbs all the light that comes towards it, reflecting nothing.
the basketball+blanket analogy is just that - a simple analogy that is intended to illustrate the idea for a simplified version of the problem. picture the same mental image for blankets at all angles with respect to the basketball. depending on what path the tennis ball is travelling in, it will follow the appropriate blanket at its angle w.r.t. the basketball. i.e. while the simple analogy is 2D, the actual effect is 3D see gravitational lensing. cheers
As others have noted, it's a 2D analogy for a 3D situation. It works because we can look at it from a 3D perspective to see the effects in a 2D world. You then have to extrapolate that to imagine what it would be like to look at it from a 4D perspective and see the effects in a 3D world. The other problem with the model is it doesn't explain why a non-moving tennis ball placed on the sheet would fall towards the basketball. Remember there is no outside gravity in the model to pull everything down. So the rubber sheet model explains why the planets revolve around the sun, but not why you are still sitting in your chair rather than floating off. The reason the model doesn't work for objects that are stationary relative to large masses is that it only models the effects of matter on space. But time is also warped by matter. Time runs slower at positions closer to a center of mass. So if you stand up and wait a moment, the time at your feet will be earlier than the time at your head. The time at your hips will be in between. Your body thus experiences a change in time relative to spatial position. Acceleration involves a change in spatial position relative to time. The two are thus equivalent and you experience an acceleration-like force - gravity - that pushes you down against the surface of the earth.
