If you were to put an oscilloscope lead on a given alternator output wire you would see a single sine wave swinging equally from negative territory to positive territory above and below the 0 volt reference line. In a 1 wire alternator you would see a single sine wave, in a 2 wire alternator you would see two sine waves 180 degrees out of phase (two phase) and in a 3 wire alternator you would see three sine waves 120 degrees out of phase (three phase). The more phases you add the higher the average output current is, as long as you gang the phases and don't set them so that they cancel eachother. The rectifier cuts off the positive alternations (negative ground systems) or the negative alternations (negative ground systems) and the Zenner diode regulates the the maximun system voltage by acting as a variable resistor (resistors can be current limiting when hung bewteen a power source and a ground, or voltage limiting when put inline). Fortunately a number of manufacturers have given us the black box (silver box?) that does both the rectification and voltage regulation.
In the US it is common to refer to 110/120V (one hot) and 220/240V (two hot) systems as single phase and to refer to 208 (three hot) as three phase, it gives the tradsmen a common langauge, but is technically quite incorrect. 110/120 V power is single phase, 220/240 is two phase and 208 is three phase. The point of having these options in a supply setting is to give the consumer choices for lowering current flow, lower current flow translates to lower supply tempatures which means less fire danger, a good thing. Ohm's law E=IR, voltage equals current time resistance; the higher the voltage the lower the current.
These same conventions have carried over to motorcycles and cars. Call it symantics, if you like, but any way you cut it: 1 wire = single phase, 2 wires = two phase and 3 wires = three phase.
The allure of a motorcycle is also it's bane