Why do voltage, current, and power go through zero 120 times per second for 60 Hz AC electricity?

Answer 1

AC power has a sine wave form.
Hz is the abbreviation for hertz, a.k.a. "cycles per second"

A complete cycle passes through zero twice.

2 x 60 = 120 cycles.

The links below each have a diagram of a sine wave.

Answer 2

I don't think average power actually goes through zero, just current and voltage. 60 Hz is sometimes called 60 cycles, which means the waveform cycles from zero to a positive peak, back down across zero to a negative peak, then across zero on the way back up.

The reason it does this is because it is typically generated from a rotating motor. A cycle is a revolution of the generator, and the magnetic fields alternately push and pull electrons in the generator coils. The pushing and pulling is what makes V and I swing back and forth.