AC power has a voltage that (in North America) oscillates high and low at a rate of 60 cycles per second.
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.
In a very small nutshell: to get continuous power but still use AC it helps if you offset the AC on several conductors. The lowest number of conductors with which this works well is three, and 360 degrees rotation offset in three equal bits is 120 degrees, hence three phase power, where each 'phase' is offset by 120 degrees from the other two. The current and voltage between the conductors are said to be 'out of phase' by 120 degrees.
