Why do powerlines usually come in groups of three?
It is called three-phase electric power. Think of alternating current as waves in water. For each cycle, you start with the wave at the neutral position (no current flowing). The wave moves up to the maximum height and then down to the neutral position again. Then down to the lowest point, and back up to neutral, to complete the cycle.
In a three phase system, the alternating current in the wires are out of sync, so that when one wire is at the neutral position, the other two are not. This provides continuous power for large motors. It also allows the production of a rotating magnetic field, which gives you a very powerful motor.
The three phase system also lets power companies send more power with less material in the conductor. That saves on copper, and means less weight for the wires to support.