What’s the meaning of “phase” as used in this article, as in a “three phases per circuit”?
Three phase AC power sends power along three wires. The timing of the oscillations on each wire is shifted by one-third of a cycle relative to the other wires, so they all reach peak voltage at slightly different times. We call this a "phase shift" between the voltages, or that the voltages are "out of phase".
If these wires were connected to a 3-phase AC motor, the motor would spin because the current is drawn in succession along one coil and then the next, leading the rotor to follow. The motor coils are also called "phases".
Each wire is sometimes called a "phase" as shorthand.
Back in highschool shop class I was tasked with building a three phase motor demonstration. The idea was to visually demonstrate the rotating field of the the three phases in the motor windings for open house. I took an old 1 horsepower (0.75kW) motor, pulled the rotor, and sat a few large-ish ball bearings in the stator housing. When plugged in to three phase the bearings rapidly spin around the inside of the stator housing.
I had to do a few more mods such as clear plexi end covers as well as add resistors in line with each phase to drop the current. Without the rotor the inductance is much lower pulling way more current than the nameplate rating (otherwise magic smoke). Then wired it to a contactor and button to run it.