Why are optoisolators often used in conjunction with solid-state circuits that control 120 VAC circuits?
Why An optoisolator couples a signal using light: an LED shines onto a phototransistor or photo-triac inside a sealed package, so the only path between input and output is optical. That means the low-voltage logic or microcontroller side shares no conductive path with the 120 VAC mains side, and isolation ratings of several kilovolts protect the control circuitry and the operator from line voltage and surges.
Watch out The impedance-related choices get it backwards: the whole point is a very high impedance (essentially infinite DC resistance) between the two sides, not a low-impedance link or impedance matching, which is a job for transformers or matching networks.
Opto = light, and light carries signal but not current. No copper path means no shock path.