The next section is where people go awry, even licensed electricians I have met. But it is also the meat of the safety aspect of the three wire configuration. We will assume a house with a single electrical panel for simplicity.
8. Three wires traverse from the main panel, down a branch circuit to the three prong "edison" outlet on the wall: One of the three prongs connects to either +120V or -120V; another connects to the EGC bar inside the panel; the last connects to the grounded service conductor bar inside the panel.
9. The short blade on the top row of the Edison connector is +120 or -120V; the tall blade on the top row connects to the grounded service conductor (colloquial neutral). The single connector on the bottom row connects to the EGC (colloquial ground).
10. If you plug in an item that has a three wire plug, the lower single plug prong will be longer. This is so that the item is electrically connected (i.e. "bonded") to the EGC before the other two wires. This insures the "fault current" path is connected before the item is energized.
11. Under normal conditions, the current path is through the item plugged in between either +120 or -120V and 0V volt potentials. Crudely think of current coming "out" the short plug prong and "in" the tall plug prong. The EGC (colloquial ground green wire) doesn't do anything under normal operation.
12. The current path is then back down the branch circuit, via the grounded service conductor (colloquial neutral). the metal bar that links all the grounded service conductors together then has a path back to 0V on the transformer by one of the three incoming conductors.
13. Finally, the current can flow from the 0V location on the transformer to the higher potential via the wire of the secondary. Notice that the GEC (earth) connection to the ground rod was NOT a meaningful component of the current path.
14. Returning to #11, and considering abnormal operation. Here current somehow flows outside of the correct circuitry in the powered item. The ECG is bonded (connected) to the item's chassis and provides an alternative current path. The EGC provides this connection back to the panel bar with all the green ECGs tied to it.
15. The EGC bus bar in the panel has a conductive link back to the grounded service conductor bus bar (colloquial neutral) via the removable link that we discussed previously. The link then "brings" the current over to the grounded service conductor (0V potential from the street), and provides the current path back through the transformer secondary.
16. Let's assume the outlet is a GFCI / RCD. It notices the current coming back on the grounded service conductor doesn't match the current going "out" into the device, and opens the circuit. That is because the fault current is "lost" to the EGC, and goes around the GFCI outlet. The outlet trips, assuming a human body is the fault current path.
17. People commonly assume that the GEC (earth) conductor somehow matters for current path in event of a fault, but this is rarely the case. Usually the water pipe or grounding rod(s) are high impedance relative to the wire in the transformer secondary, and so the current divider formed is essentially all through the grounded service conductor.
18. The GEC (earth) connector holds the pole transformer secondary center tap near the same relative 0V potential as the house. The GEC may also provide the lower impedance path at very high frequencies encountered during a lightning strike.
If you made it this far, I'm happy to field further questions :-)