3 phase motors (and generators) are more compact and lighter above a given HP (or KW) rating. 3 phase equipment makes more efficient use of power than single phase motors/generators.
3 phase motors also run smoother, start up with more torque than their single phase counterparts and are more reliable.
A single phase current crosses zero twice per cycle and has two peaks.
One negative and one positive.
With 3 phase power, these peaks and zero crossing points are staggered:
The graphics above should illustrate how 3 phase current can provide a broader area of max power transfer than single phase current.
411A mentions the original inverters - converting power by driving a generator with a motor. This is why we refer to current day electronic inverters as
static.
Blah blah blah...
During a summer job at a plastics factory belonging to a friend of the family, I learned wiring of 3 phase motors was fairly simple - if you got it wrong the motor would just spin backwards - swap any two power wires and you're in business.