You can do lots of things with it, like: adjust the input line voltage of a circuit to spec;
bring up a circuit slowly to allow old capacitors to burn in; check for circuit stability
when powering up/down or with line sag/boost; test circuits that need lower input voltages
than the AC line, without a step down transformer.
In troubleshooting, especially solid state units, I can bring up the mains gently, and watch for current ramping up (indicating trouble) before applying full power to the circuit. This is similar in purpose to the famous light bulb limiter.
More reliable than a light bulb limiter as one can deliver as much current as required. I bought, some years ago an industrial 3kVA variac, so nothing is a problem at any voltage from low to 270V for me and have used it in my workshops since 1980.