First thing to understand is AC power. It's a voltage that varies at 60Hz in a sine wave. The key thing about this is that since it's a wave, you can have different phases that provide different amounts of power.
You've heard of 'single-phase' and 'three-phase' power?
Single-phase means there's two hot wires carrying the power, with sine
waves that are 180 degrees out-of-phase. (Only one phase difference, so
it's only single phase.)
Three-phase has three hot wires carrying power in sine waves that are 120
degrees out-of-phase from each other. Since there's three possible phase
differences (compare any one of the three hot wires to any other of the
three) it's called three-phase.
How you doin' so far?
The cool thing (I think) is that since there's always another wire that's at zero volts (called the neutral wire) you can have one voltage if you connect between two hot wires, and another voltage if you connect between any hot wire and the neutral wire.
Even more cool: If you have three hot wires (three phase power) that can
deliver 20 amperes each, you don't have to have the neutral wire
able to handle 60 amps - the neutral wire only carries 20 amps at most
because the currents from each hot that are flowing through the neutral
are 120 degrees out of phase!
Get it?