With a single phase, the voltage drops to 0 every half-cycle. Therefore, the amount of power you can get out of the line is not constant over time; it has a very large 120-hz ripple. With a large motor, this can cause vibration, and also means that larger wires are needed for the same power load. The same is true for so-called "2-phase" power, 2 voltages 180 degrees apart. They both cross zero at the same time, which is why this is normally also referred to as single-phase. It isn't any better than single phase. With 3-phase power, however, there is never a time when all the voltages go to 0. In fact, if you are extracting power from all 3 phases, (like in a motor) the power stays constant throughout the whole cycle. This gives a vibration-free drive (and also allows for simpler motor design because 3-phase power has an inherent "direction" which 2-phase or 1-phase power does not).
Think of it like pedaling a bicycle. With single phase, it's like your only have 1 pedal. So you only do work while pushing the pedal down. If you have 2 pedals, one foot can apply a force while the other is going up doing no work. 3 phase is similar to that but there's 3 "pedals" each being "pushed" at different times so they work together to create more power.
Even for a DC application, where you're rectifying the output voltage (like in a car alternator) 3-phase is better. Although you're only pulling power from one phase at a time, the voltage still never goes to 0; it only ripples down to about 70% of its full-scale value before the next phase picks up. With single phase there are 2 zero crossings in every cycle. At the zero crossing there is no power available for the load. With 3 phases the zero crossings are staggered so there is always power to the load. This true for motors, but also for DC rectified loads. High power television and radio transmitters use 3 phase for the DC supply for greatly improved efficiency.
So you can use star and delta configurations. Star for start for high torque then delta for running once the motor is up to speed. You transfer the most power with the least copper and least losses that way. For example: A three-phase AC motor has only the bearings as moving parts. The only electrical component is the stator which is just three stationary coils of wire. These motors, when applied correctly, typically last for a decade or more in operation. A single-phase motor, on the other hand, has to be designed to compensate for the lack of starting torque inherent in the circuit. There are many ways in which this can be accomplished, but in every case there are drawbacks that are not present in the 3-phase system