All of us have done it at some time or another; we've had the battery in our automobile go "dead" on us, requiring us to ask a friend, neighbor, or relative for a jump start. Most of us take it for granted, not considering what's actually going on here.
All you do is pop the hood of one car, take a pair of jumper cables, and connect together the positive battery ends and the negative battery ends. Start the good car, wait for a few moments for the energy to distribute, then start the bad car, and you've then jump started the weaker car and solved your problem.
When you jump start your car, you are actually creating a simple parallel circuit. The two negative battery ends are connected together by a cable, as are the two positive ends. A parallel circuit only works correctly if both batteries have the same electromotive force; luckily, all car batteries operate on 12 V of power, which is produced by a specific emf, so car batteries are compatible.
Mixing batteries with different voltages will cause an explosion. Automobile manufacturers, for ease of assembly and maintenance, decided that one specific voltage should be standard for virtually all automobiles, and the battery manufacturers of course complied. The dangers of mixed voltages is the reason you can be electrocuted... and the reason that it's safe to jump your car.
Here's a look at the circuit in a generic sense. The dashed lines indicate the connecting cable.
|-----(+ battery of good car -)-----|
|-----(+ battery of bad car -)-----|
When the "good" automobile is started, it begins to pump energy into the circuit, which is passed to the dead battery through the cables. Since the two + sides and the two - sides are connected, the cable attempts to make the charge in both + sides and, distinctly, the charge in both - sides equal. Once the weaker battery has enough power to operate the starter motor, then you are able to start your car. At that point, circuits inside your own car utilize power produced by the engine to charge your battery.
Note: Don't do the following, period! If you must do them, neither I nor e2 have any responsibility for your personal safety nor the safety of property around you. This can be seriously dangerous, folks!
If you want to see something truly frightening and a clear demonstration of why you should be careful when doing a car jumping, go to your local hardware store and purchase five nine volt batteries, some copper wire (preferably with rubber coating), and a six volt battery. Take these home, and hook up a circuit like the one above (connecting the +'s and -'s). You might want to place a shield between you and the batteries and wear gloves if you do this; I don't recommend it, myself. Once they're connected, back a fair amount away and wait for one of the batteries to explode.
You can perform similar tricks by hooking up the same voltage batteries in bad orientations. Effects such as smoldering and glowing wires and other such things will occur. I burnt myself quite badly doing stunts like these as a young child.
In essence, your car battery is a powerful but simple parallel electrical circuit. Like any other circuit, you should treat it with care.