Today, most electrical devices are "grounded", meaning that one of their power wires is connected to another wire. The ground wire normally does not carry any electricity; It only does when it is actually serving its purpose of alleviating dangerous situations. Although most people understand that grounding is for safety, they do not really understand how it is done or what it is supposed to prevent. In this light, then, a simple explanation of how and why grounding is done is offered here.
In DC electrical circuits, it is almost universally standard to make the negative side the grounded side. Most cars follow this convention as well: The car's negative battery terminal is actually connected to the body of the car, and the car body then becomes the path by which electricity passes from one battery terminal to the other. This is not to say that every single car in the world is negative-ground; There *are* positive-ground cars in existence, but they are rare and regarded rather strangely.
AC circuits do not have a positive or negative end, since their polarity is constantly reversing; Instead, they have "hot" and "return" wires. In modern household wiring, the "return" wire (also known as the "neutral" or "common" wire) is always connected to ground because there is no voltage on it, while the "hot" wire is connected to the circuit breakers (or fuses) and the wall switches.
In the United Kingdom, ground is called "earth"; "Ground" is usually North American terminology.
It is important to understand that grounding is not actually necessary for an electrical device to work correctly, and in fact the device will be perfectly safe under ideal circumstances without grounding. However, sometimes circumstances become less-than-ideal, and grounding exists precisely for when unsafe circumstances do come up.
Electrical appliances like washing machines and vacuum cleaners do not normally need to be grounded, and in fact in the old days they were not, because the wires inside do not normally touch the casing of the device, and so people touching the case are not exposed to any kind of electricity. This kind of case, which does not come into contact with any wires, is called a "floating case". However, even floating cases are normally grounded nowadays, simply because wires can and sometimes do break off or get moved around by vibration, which could theoretically cause them to touch the casing. This is entirely theoretical, but the danger is real enough to warrant precautions. It has happened, and will continue to happen on an occasional basis.
Grounding also helps protect people (and devices) in short-circuit cases. If two wires inside a device happen to touch each other, a short circuit may result, which could start a fire and would likely damage the device. The ground wire provides an alternate path for the electricity to flow through. In a very similar way, grounding helps prevent danger from overvoltage caused by lightning or power surges.
Grounding also serves another purpose which is not really related to safety: It provides a common reference point for voltage. If an electrical device's only connections are to the two ends of its power source, it is electrically unstable and the voltage levels may vary. Neither one would be at zero volts. Because planet Earth stays at a common voltage, it provides a universal voltage reference point. (The planet is usually considered to be at zero volts, even though this is not perfectly true, as Earth itself is something of a conductor.) This is especially important when using sensitive electronic devices like computer circuits which are very picky about the voltages you supply them. Feed a chip with 3 or 7 volts when it wants 5, and the whole thing may stop functioning entirely.
In small-scale electronics, circuits often are illustrated as having "positive" and "ground" ends, rather than "positive" and "negative". Instead of actually having a negative voltage for the return path, ground (which has a voltage of approximately zero) is simply used, and the difference between zero and whatever positive voltage is used is what drives the circuit.