How AC current is distributed to our homes?
Actually, current is not distributed to our homes.

Instead, voltage is distributed.

The AC voltage (alternating voltage) is sent to distant consumers.  If they wish, they can connect various loads (resistors) across the pair of wires, and then these resistors draw a current from the system.

Or in more detail:  the generator charges the two wires as if they were capacitor plates.  A momentary current appears, and in this way some electrical energy flows into the wire-pair and is stored as e-fields in the space between wires.  Next, when a distant consumer connects a load resistance, this load then discharges the wire-pair.  A momentary current appears, and the electrical energy flows from the wire-pair and into the distant appliance.  The voltage across the wires starts to decrease as the wires become discharged.  The generator at the other end will see this falling voltage, and will then re-charge the wire-pair to bring the voltage back up again.

Use of energy by the consumer is a give-and-take process between the generator charging up the wires, and the consumer discharging them.  In such a "constant voltage system," each distant appliance acts like a "leakage" between the oppositely-charged wires.  The voltage across the wires remains constant, while the conductors' charges are flowing in proportion to the number of appliances which are turned on, and their parallel resistance (the amount of "leakage.") 

Notice that the term "constant voltage system" applies to both AC and DC.  

By "constant voltage" we mean constant-voltage-variable-current, where the generator produces a particular voltage, and then the distant consumers can draw any current, including zero.

But yes, as you might suspect, some very early experimental systems used constant current instead of constant voltage.  (Constant-current-variable-voltage.)  In those systems, everything was backwards: all the distant appliances were wired in series, not parallel, and you'd short out an appliance in order to turn it off.  (Typical appliances were arc lamps, or non-carbon metal-filament light bulbs.)  In those systems the AC generator really did send out current to all distant users.  High current, at low or zero voltage depending on how many appliances were switched on.  Then the consumers could draw energy from the grid by un-shorting an appliance and allowing it produce a back-voltage.   This power grid, rather than being like a pair of charged wires (a capacitor,) instead would be a closed loop of wire with a large circulating current (an inductor.)  And, to "discharge" an inductor, we insert a resistor into the closed loop.   In a constant-current system the current is always the same, and the distant consumers can create whatever voltage they need, including zero.

PS

Electric circuits are nearly impossible to visualize unless we've been taught that all wires are already full of movable electricity, while batteries and generators are "electricity pumps."  This is the charge-centric explanation, also called Hydraulic Analogy, or "full pipes scenario."   A generator is a charge-pump which pulls electricity in through one wire, then forces electricity to flow through the generator coils and back out through the rest of the circuit.  If wires are like blood-filled arteries, then a battery is like your heart, and electrons are the blood cells.  The heart does not produce any blood, just as generators can never "generate electricity."  Instead, batteries and generators just pump electricity in a closed-loop flow, and the total quantity of electricity in the circuit is not changing.  The electrons (the movable electricity) is supplied by the conductor's atoms: it's the so-called "sea of charge" found in all metals.