| I'm not trying to pull an Edison. Specifically, what makes 3-phase more | efficient | than single phase?
We have to consider 2 reasons to use three phase power. One is because there are demands/needs for three phase power, such as very large motors. That may or may not be more efficient. But you can't serve those needs unless you have the phases. You can get single phase out of three phase easily, but not the other way around. The other is because of efficiency even if the loads are all single phase (evenly balanced on three phases).
But let's consider a case of efficiency.
Comparing 3-phase power to a 2-pole single phase system (which looks like it could be called "2-phase" but that isn't standard terminology): If you have a need for 600 kW of power, you could get that by having 200 kW on each of 3 line wires, or 300 kW on each of 2 line wires (pick your own voltage to figure the amps). For the line wires alone, it works out basically even, if cross sectional area of wires equates to cost, and in large scale systems it does. However, unless all your loads are only line-to-line loads, you need a neutral wire, too. Potentially it could see the full current a line wire could see, in the most unbalanced case (before assumping harmonics or differential power factors). So that neutral will need to have the same size as the line wire, which will be
50% larger in the single phase case.
Consider another case.
For a given line-to-neutral/ground voltage, the line-to-line voltage will be higher in single phase, and in certain circumstances require a higher level of insulation. Or considered in reverse, for a given level of insulation that handles line-to-line voltages, three phase lets you have a 15.47% higher voltage (and thus get more power with the same amps) over what you can do in single phase. This would apply even if the load does not need a neutral and it is not carried over the wiring.
I don't know enough about motors, yet, to tell you how they might be more efficient in three phase than in single phase. But I know that as the motor power goes up, the probability a given installation uses three phase over single phase also goes up. But this could be due to issues that are similar to the cases for transmitting and distributing power.
| Is it that you can kinda, sort of have a complete circuit with only one | wire?
No.
| Or, that you can have three complete circuits with only three wires | instead of six?
You can have 3 "circuits" with 4 wires, vs. 2 "circuits" with 3 wires.
| Remember, I am pre-admitting ignorance, so you don't have to tell me how | ignorant I am.
I'll refrain. We all started there at some point.