A singularity refers to a point or region in the space-time continuum where normal physical patterns do not apply; the term is derived from mathematics. An extraordinary amount of gravitational forces are typically present in singularities, though, they can be both natural and artificially generated. A gravitational singularity refers to a point of infinite or near-infinite density or space curvature.
A black hole is an object with such powerful gravity that nothing can escape from it, including light. The black hole's mass is concentrated in a point of almost infinite density called a singularity. At the singularity itself, gravity is almost infinitely strong, so it crushes normal space-time out of existence. As the distance from the singularity increases, its gravitational influence lessens. At a certain distance, which depends on the singularity's mass, the speed needed to escape from the black hole equals the speed of light. This distance marks the black hole's "event horizon," which is like its surface, surrounding the singularity. Anything that passes through the horizon is trapped inside the black hole. A rotating black hole is surrounded by the ergosphere, a region in which the black hole drags space itself.
Black holes come in several varieties, depending on mass. Although black holes come in a variety of masses and sizes, their structures are all alike. The singularity forms when matter is compressed so tightly that no other force of nature can balance it. In a "normal" star, like the Sun, the inward pull of gravity is balanced by the outward pressure of the nuclear reactions in its core. In the collapsed stars known as white dwarfs or neutron stars, other forces prevent the ultimate collapse. If there is too much mass in a given volume, though, the object reaches a critical density where nothing can prevent its ultimate collapse to form a black hole.
Because gravity overcomes the other forces of nature, a singularity follows its own bizarre rules of physics. Time and space as we know them are crushed out of existence, and gravity becomes infinitely strong. As the distance from the singularity increases, the escape velocity decreases. Escape velocity is the speed at which an object must move to get away. For Earth, the escape velocity is around seven miles (11 km) per second. In other words, a spacecraft must go at least that fast to escape Earth's gravitational pull and travel to another planet.
At a certain distance from the singularity, the escape velocity drops to the speed of light (about 186,000 miles/300,000 km per second). This distance is known as the Schwarzschild radius, in honor of Karl Schwarzschild, who first defined it. This radius depends on the mass of the black hole. For a black hole as massive as the Sun, the radius is about two miles (3 km). For every extra solar mass, the radius increases by two miles. This radius enfolds the singularity in a zone of blackness - in other words, it makes a black hole black. It gives the black hole a visible surface, which is known as the "event horizon". This is not a solid surface, though. It is simply the "point of no return" for anything that approaches the black hole. Once any object - from a starship to a particle of light - crosses inside this horizon, it cannot get back out. It is trapped inside the black hole. Anything that enters the black hole increases its mass. And as the mass goes up, the size of the "event horizon" gets bigger, too. So if you feed a black hole, it gets fatter!
If the black hole doesn't rotate, then its gravitational influence on its environment is straightforward. If the black hole is spinning, though, then its gravitational effects are more complicated. It actually pulls the fabric of space/time along with it - an effect called frame dragging. This area is known as the ergosphere. Seen in cross-section, it is oval-shaped, with the region of influence extending farther into space at the black hole's equator than at its poles.
Nothing that falls into a black hole can come back out again -- at least not in its original form. But a black hole may lose some of its mass. Quantum theory says that "virtual pairs" of particles sometimes wink into existence from the fabric of space itself. These particles quickly cancel each other out and vanish. But if a pair of particles appear just outside a black hole's horizon, one may fall inside, never to make it outside again. If the one on the outside doesn't fall through the horizon, then the particles can't cancel each other out. In essence, that "steals" a little bit of mass from a black hole. Over countless billions of billions of billions of years, the mass loss could become substantial enough to cause the black hole to vaporize. Material would come out, but not in its original form -- only as energy and subatomic particles. This energy is known as Hawking radiation in honor of Stephen Hawking, the physicist who first described it.
White holes are VERY hypothetical. They are, in fact, predicted as a possible "other end" of a black hole that has punctured a "worm hole" through space, but black holes are most likely just a point in space without another side. The matter/energy coming out of white holes is supposedly the matter falling into a black hole. They've only been discussed in theoretical physics talks. At one point scientists speculated that quasars may be white holes, but now they are fairly certain that quasars are powered by supermassive black holes, in which case the light we see comes from matter as it falls into the black hole. After it falls in, we assume the matter just becomes part of the black hole and does not come out anywhere.