Purposes of Grounding

Grounding system has three main purposes:

Overvoltage protection

Lightning, line surges or unintentional contact with higher voltage lines can cause dangerously high voltages to the electrical distribution system wires. Grounding provides an alternative path around the electrical system of your home or workplace minimizes damage from such occurances.

Voltage stabilization

There are many sources of electricity. Every transformer can be considered a separate source. If there were not a common reference point for all these voltage sources it would be extremely difficult to calculate their relationships to each other. The earth is the most omnipresent conductive surface, and so it was adopted in the very beginnings of electrical deistirution systems as a nearly universal standard for all electric systems.

Current path in order to facilitate the operation of overcurrent devices

This purpose of grounding is the most important one to understand. Grounding system provides certain level of safety to humans and property in case of equipment damages.

Grounding operation in electrical distribution network

The main reason why grounding is used in electrical distribution network is the safety: when all metallic parts in electrical equipments are grounded then if the insulation inside the equipments fails there are no dangerous voltages present in the equipment case. Then the live wire touches the grounded case then the circuit is effectively shorted and fuse will immediatly blow. When the fuse is blown then the dangerous voltages are away.
The safety is the primary function of grounding. Grounding systems are designed so that they do provide the necessary safety functions. Grounding also have other functions in some applications but the safety should not be compromised in any case. Grounding is quite often used to provide common ground reference potential for all equipments but the existing building grounding systems might not provide good enough ground potential for all equipments which might lead to ground potential difference and ground loop problems which are common problems in computer networks and audio/video systems.

How electric shock happens

The "hot" wire is at 120 volts or 230 volts (depends on the mains voltage used in your country) and the other wire is neutral or ground. If a person were to touch the neutral wire only, no shock would result simply because there is no voltage on it. If he were to touch the hot wire only, again nothing would happen to him unless some other part of his body were to become grounded. A person is considered to be grounded if he comes in contact with a water pipe, metal conduit, the neutral or ground wire, or stands barefoot on a concrete floor.
In other words, neither wire is a shock hazard unless a person is grounded, and then only the hot is a potential shock hazard. Of course, if a person were to touch both wires at the same time, he would be shocked simply because his body is completing connection between "hot" and "ground" wires.

Metal case safety

Back in the early days, equipment and appliances fitted with the two wire power plug were readily accepted to be safe from shock hazard because the metal housing was not connected to either wire of the line cord (called floating case).
One of the problems with appliances and equipment which have a "floating metal case" is that a shock hazard exists if the case comes into contact with the hot wire. This so called "fault condition" may happen in many ways with some of the more common causes being a "pinched" line cord, failure of installation systems, or movement of components due to shock or vibration which will cause the "hot wire" terminal to touch the case.
Naturally, if for any reason the case does become "live,"then a person touching it may be shocked if he is grounded. If this "hot chassis" is connected to another chassis or instrument by a typical shielded cord, then that chassis or instrument will become hot also. The entire purpose of the present three wire system is to provide a separate ground path which will effectively eliminate any possibility of shock.
If the live wire touches the grounde metal case the ground connection in the case causes that the situation becomes a showrt circuit as drawn in picture below.

This short circuit situation causes very high current surge to flow in the circuit which will cause the distribution panel fuse to blow almost immediatly. The cureent in short circuit situation can be pretty high because of the low resistance of the mains distribution wiring.
The integrity of the separate ground path is directly related to the quality of the chassis/green wire/ground pin combination. When the ground pin is removed, the separate ground path is destroyed and then fault conditions may cause shock hazards.

Grounding and interference susceptibility

Whenever audio equipment is operated without a ground (floating chassis), strange things can happen. Under certain conditions the amplifier will be more susceptible to radio frequency interference (picking up radio stations or CB. radio). Also, without a suitable ground, amplifiers sometimes "hum" more when the musician picks up his instrument and provides a "pseudo" ground through himself.
The only solution is to find a ground point to connect to the chassis. Sometimes this may just cause more problems than it helps.

Grounding in wiring

Today's modern (US.) mains cable consists of three separate wires: black, white, and green. The green wire is always connected to the large ground pin on the plug, and the other (green) end connected to the chassis of the equipment. The black wire is always considered to be the "hot wire," and as such, is always the leg which is connected to the switch and fuse. The white wire is always the neutral or common wire.
European coloring is a little bit different. The ground wire is here green wire with yellow stripe. Neutral wire is blue. Live wire in Brown (additional colors for the live wires used in 3 phase systems are black and black with white stripe).
Any modification of the above 3 wire mains system completely eliminates the protection given by the three wire configuration. The integrity of the separate ground path is also directly related to the quality of the receptacle and the wiring system in the building itself.
The neutral (grounded conductor) must be solidly connected (bonded) to the home's ground system at the first disconnect (main panel). This keeps large voltage differences from developing between the neutral and ground.

Currents in grounding wire

Ground wires should not carry current except during faults. If the ground wire carries any current there will be a potential difference between different grounding points (bacause the current flowing in wire causes voltage drop because wire resistance). This is why a common wire which works as neutral and grounding wire is very bad thing.
When there is separate wiring for grounding you can't still completely avoid the current flowing in grounding wires ! There will always be some capacitive leakage current form the live wire to the ground wire. This capacitive leakage current is caused by the fact that the wiring, transformers and interference filters all have some capacitance between the ground and live wire. The amount of current is limited to be quite low (limited to be between 0.6 mA to 10 mA depending on equipment type) so it does not cause dangers and big problems. Because of this leakege current there is always some current flowing in the ground wire and the ground potentials of different electrical power outlets are never equal.
The leakege current can also cause other type of problems. In some situations there are ground fault detect interrupter (GFCI) circuits in use the leakage current caused by many equipments together can make the GFCI to cut the current. Typically GFCI circuits are designed to cut current when there is 30 mA or more difference in currents flowing in live and neutral wires (the difference of those current must flow to ground). Some GFCI circuit can cut the mains feed even at 15 mA leakage current which may mean that if you connect many computer equipments (each of them having 0.5 to 2 mA of leakage) to GFCI protected power outlet you can cause the GFCI to cut the power feed.

Ground wire resistance

In europe it is not important how much ohms the grounding is but the maximum current before the unit switches off is important. So a grounding of 230 volts and a safety of 24 volts. We say it must be less then 30 mA in our body. So for 16 amps and 24 volts it is 1.5 ohms. This means that the maximum voltage on the case is 24 volts even when all current is flowing thru the grounding wire. In places where even this 24V is considered very dangerous (for example in hospitals) the ground resistance must be made lower to make sure that there is never dangrous voltage present in the case. For example in Finland the grounding resistance for medical room outles must be less than 0.2 ohms to be considered safe.
The above is the objective, and all the crap around it is just to make it difficult. Ground means something connected to the surrounding and it must be less then x ohms measured with AC and the wire must handle the short circuit current present in the circuit without overheating.