Picture yourself on the surface of the Earth (or in a boat on a river). Now, if you were to toss something up into the air, it would eventually be pulled back down, due to the effects of gravity. Obviously, this force is not indomitable, as we've escaped the Earth's gravitational well many a time (most recently, when we sent something awesome to Mars—because orbit doesn't really count as escaping the Earth's gravity). In fact, if you were to toss something up with enough force, it would fly away forever, never to be seen again. The speed you instantaneously imparted on that object when you threw it is the Earth's escape velocity. Now, let's say we increase the mass of the Earth to that of Jupiter, but keep the size the same (we make the Earth much, much more dense). Now, in the instant before you were liquified by it, you'd notice the gravity has become much, much stronger than it was. This makes perfect sense, as gravity is a property of mass. Now, you would also note that it would take a much higher speed to escape this new, obscenely dense Earth. The escape velocity of the planet would keep increasing as a function of the mass (because of the gravity increase), and, because this doesn't asymptote, eventually you could be standing on the surface of a planet whose escape velocity exceeds that of the speed of light. If you were to shine a light upwards from the surface, it would never, ever be seen from outside the planet. You are now inside a black hole (and also dead, because you're inside a black hole).

See, every massive body in the universe (so, everything that is comprised of matter) has something called a Schwarzschild Radius. This is a radius at which the escape velocity from that body is greater than the speed of light. For almost everything in the universe, that radius is minuscule. However, if the Schwarzschild Radius of a body ever subtends the actual, physical radius of that body, it is a black hole (or maybe a so-called Newtonian Dark Star, but we won't get into that here). This radius is also often called the black hole's Event Horizon, the "invisible" line which denotes the beginning of the black hole. The mass itself is called a singularity, as it isn't quite as simple as a planet, it's actually an infinitesimal point with a outlandishly high density.

When a sufficiently massive body, such as a star much larger than our own sun, finally exhausts all its fuel, it can no longer sustain the fusion reactions that keep it stable, and it begins to collapse under its own gravitational forces. Now, stop reading this for a moment, and drop something to the floor next to you. Did you notice how, when it hit the floor, it stopped (or even bounced back up)? That's because gravity is pretty weak, in relation to the forces that hold together atoms and molecules (nuclear forces and electromagnetic forces). However, gravity scaled like no one's business. If you have enough mass, the combined gravity of that mass can become greater than the bonds which hold together molecules, and the electromagnetic forces that keep atoms in their shape, compressing together all the mass of the atom into the nucleus, and smooshing together protons and electrons into neutrons (this is because the the gravitational force exceeds electron degeneracy pressure). At this point in a star's collapse, it may stop, because there is a force, called neutron degeneracy pressure, which holds up neutrons from collapsing into their constituent quarks and compressing further. If it does stop, it becomes a Neutron Star, which is a star composed of one giant atomic nucleus, with a super awesome quark-gluon plasma at the core of it. But we can go further. If our mass is still, well, massive enough, it will collapse the neutrons as well, and then no force in the universe can stop it from collapsing further and further, condensing into a single infinitesimal point still containing all that mass, called a singularity. At this point, its Schwarzschild Radius obviously exceeds its actual radius (which is approaching zero), and it has completed its transformation into a black hole.

Usually, though, the singularity isn't a point, because stars have a tendency to spin, and that spinning continues and intensifies as it collapses. This causes the point to actually stretch out into a ring, or torus shape. Just a fun fact. Another fun fact is the existence of tidal forces.

Tidal forces are more or less the effect of having two drastically different amounts of a gravity over a short space. Let's saw we have a tiny black hole that has the equivalent of Earth's gravity from one meter away. Now, what would happen if you were to attempt to reach out and touch it? The answer is simple: you would be torn to pieces by tidal forces. See, gravity scales at a factor of 1/r² (the full formula for calculating the force of gravity between two bodies is g=G(m₁m₂)/r²). That means that the gravity at one meter away is four times greater than the gravity at two meters away, and the gravity at half a meter away is four times greater than that (and so on). This results in the effect that, as you reach out your hand, your hand is feeling several times Earth's gravity, while your arm is feeling something like the moon's gravity. Which ruins both your day and your arm.

As a final note, despite their names, black holes are not actually black. They radiate. They do not, however, radiate in the conventional sense (through black body radiation), as that light would be incapable of escaping. This kind of a radiation is called Harking Radiation, after the physicist Stephen Hawking, who postulated it. Basically, it sums to this: weird, bizarre things happen in space on a quantum level. Less basically, it can be described thusly: In any system with energy (like space, or a black hole) a subatomic particle and its corrosponding antiparticle (such as a quark and an antiquark) can spring into existence, borrowing energy from the system to do so (E=mc²). After this, they are supposed to collide with each other, which results in annihilation, and all the energy from that mass it returned to the system that it borrowed it from. However, if this happens on the event horizon of a black hole, borrowing energy from the black hole itself, the particle (or antiparticle) may escape, while the other falls back in, stealing away some energy (and therefore also mass, becayuse they're one and the same) from the black hole. This process can eventually completely evaporate a black hole, albeit very, very slowly. So don't count on it stopping a black hole when you're falling into it. Just try to stay away from black holes in general, they're not fun places to be.