Simply; your live wire is tied to a power source. Neutral is ultimately tied to ground. If neither wire is connected to anything (like a bulb), then, in a normally wired house, the live wire will have 120VAC on it (in the US) and the neutral would be at 0 VAC. Now if you hook up a bulb in the circuit, the neutral and live wires will be carrying the same current, but if you check the voltage on the LIVE side of the bulb, you will see 120VAC, and on the output side, 0 VAC (a little more, actually, since the wire itself acts as a resistor). The big danger exists when, for any reason, the neutral becomes disconnected from ground; then you've lost your current path, the bulb fails to illuminate, and the neutral becomes hot in the circuit. All neutrals in all circuits are normally supposed to have a return path to ground, and the neutral path should never, ever be used as a switch-break - that should always be on the hot side.
The third wire, the Earth, or Ground, is green in the US. Like the neutral, it also returns to ground, but unlike the neutral, it is never supposed to carry any current, except in the unlikely circumstance that you have a wiring problem, which is why this wire is usually connected to the metallic outer sleeve of whatever object is being powered; if there's a loose wire inside, it will go to ground before it electrocutes you.
Three phase systems are another type of beast, in that you can get all your power in a system using phase-to-phase currents, and don't need to use your neutral at all (ideally). In a perfect 3-phase motor, your neutral current would be zero. The neutral, however, is still ultimately tied to ground.
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