Loads that span all 3 phases are generally motor loads that will benefit from the rotating magnetic field that 3-phase service provides -- such as pumps and compressors.
3 phase power to residential is rare in the US.
Residential power in North America is usually delivered as "split phase", +120V, neutral, and -120V. (180 degrees out of phase: https://www.youtube.com/watch?v=vOh2OSJ44eE) The voltage across the two hot conductors is 240V, which is used for big stuff. You get it by tapping a transformer in the middle of a coil: https://en.wikipedia.org/wiki/Split-phase_electric_power
Three phase power has three hot conductors, 120 degrees out of phase to each other. In the US it can be delivered at a bunch of different voltages, depending on what transformer the customer installs, but generally I worked with 277/480. (277V hot to neutral, 480V hot to hot. Generally all commercial lighting runs on 277V.)
And to be specific, three phase is primarily useful because motors that use it are self-starting, you don't need to capacitor-and-switch arrangement single phase motors use, which frequently break. Less important now that most big motors use VFDs. Also, supposedly due to some frequency voodoo you don't need to use as much cable when running three phrase transmission cable.
As to the benefit to motors, it was my understanding that using split-phase or a single phase and a capacitor creates a less-than-optimal magnetic field which results in more noise/vibration and wear on the motor as opposed to 3 phase.
This setup is pretty much a mess, and can wreak havoc on laboratory setups, so e.g. at universities all the lab rooms are laid out with TN (the standard everyone else uses). This means you can mess stuff up in the lab by running an extension cord from the adjacent non-lab room (e.g. get large ground voltage differences, all sorts of wanky stuff).