Why there are live and neutral wires attached to house's wall sockets
There must be two wires for a complete circuit.

Now, in a balanced AC circuit, both wires provide an alternating voltage with respect to ground (earth).  When one wire is positive, the other is negative.

However, in an unbalanced system, one wire is neutral, which should ideally be at 0V with respect to ground, and the other is hot which alternates positive and negative with respect to ground.

In either case, both wires have (ideally) equal and opposite current.

If I'm not mistaken, in the USA, the neutral and ground are connected together at the meter base (service entrance).

For a generator that isn't referenced to ground, the AC voltage is simply across the 'hot' and 'neutral'.

There are devices for converting unbalanced AC to balanced AC power.