It's AC; the voltage on each leg is constantly changing. When one leg is at +120V, the other leg is at -120V, relative to ground, because they both come from a center-tapped transformer on the pole outside the house. The center tap of that transformer is grounded.
Inside the house, within the fusebox, the two hot wires feed separate buses. The third, bare bus within the fusebox is where all the house's neutrals are tied together, and is the one point where the neutrals are also tied to a ground, usually a short bare wire attached to an actual metallic rod in the ground.
120V appliances connect to one of the hot wires and to the neutral bus. Within those appliances, electrons come in on the hot wire and leave on the neutral wire. Then they come in on the neutral wire and leave on the hot wire. Because the neutral is forced to (near) ground potential by the bus tie within the fuse box, it's only necessary to break the hot wire to render an appliance safe.
240V appliances connect to both hot wires. Electrons come in on one hot wire and leave on the other, just as you describe. Then the current turns around, and the cycle repeats. Because both hot wires are 'hot', not near ground potential, it is necessary to break both hot wires to render the appliance safe. That's why 240V breakers have two poles.
Safe, in the context noted above, is a relative term. If a circuit is damaged in such a way that a hot wire connects to the appliance frame, that's when the ground wires get involved, and force the frame voltage to near ground. This usually forces a breaker to open and remove the voltage from the hot wire.
All of the above applies to the USA, Canada, and some other places in the world. In Europe, there's no neutral wire at the appliance; everything is 240V, or at least not 120V.
The above is offered without warranty, and is my current misunderstanding of how USA house wiring works.
Mike Halloran
Pembroke Pines, FL, USA