Earth Ground's role in 3 prong AC systems
AC power distribution systems are two wire circuits for delivering the current to the load. The hot wire conducts the current to the load on the positive AC cycles and from the load on the negative AC cycles. The "neutral wire" is used to conduct the corresponding current from to the load. It conducts current from the load on the positive AC cycles and to the load on the negative AC cycles. The use of the two conductors (Hot and Neutral assures a low resistance circuit path to make the distribution as efficient as possible).

For safety reasons and attempts to stabilize a local reference for the AC power distribution network the "neutral wires" are connected (bonded) to an actual earth ground connection at the entrance to the facility. This means that any given time there is a potential current path from the hot wire through a person's body to anything that is part of the nearby earth ground, be that through wet dirt, damp concrete, water pipes that go into the ground, metal building structures that are buried to foundations in the ground and even water paths to the ground. Any such current that is over some threshold through the human body is lethal. To mitigate this danger the standardized and codified electrical systems in most countries and regions these days require that all AC power distribution systems provide for a low impedance additional conductor path (safety ground) from the usage point (outlet for example) back to the facility entrance point where these additional conductors are tied in common to earth ground and to the "neutral wires". This low impedance path is intended to be connected to any thing that the user may be able to touch that is conductive on an appliance or fixture. The idea is that if there is some type of accidental short from the hot connection inside the appliance to the metal parts of the unit that people can touch that any current that wants to flow would take the preferential path through the safety ground wires back to the service entrance as opposed to going through the person and back through some other path. 

These days many circuits in homes and businesses that are located near water, water pipes and other grounded metal systems are required to be equipped with ground fault circuit interrupters (GFCI). These units are designed to constantly monitor the current on the circuit and compare if the current on the hot side of the circuit is within 5mA of the current flowing in the "neutral wires". If they differ by more than this amount then the GFCI trips and open circuits the load point from the power feed. An imbalance could happen in cases where some person touched some metal part of an appliance or fixture where there was a fault or insulation breakdown. Some current could go through the person and into the nearby earth ground network back to the service entrance. Any current over 5mA is considered potentially lethal and so the GFCI trips to protect the user. 

Note that not all appliances and devices are equipped with three prong power cords to take advantage of the safety ground feature. Such devices these days, that are manufactured and distributed by honest and reliable businesses, will be designed in such way that it is deemed safe to use the device even if there is an internal short or fault associated with the hot wire connection. These devices often have external plastic cases and are sometimes referred to as being "double insulated".