Use a relay to;
Switch high voltage/current with safer/ more economic/ smaller/ lower voltage/ control circuit components, say in power transmission. Or, mixed voltage circuitry; controls= lvdc, power= higher vac.
Switch multiple circuits with no backfeeds.
As for example a heating boiler may be fired by signals from multiple programmable zone thermostats or timers, without backfeeding the thermostats/timers themselves or operating all the solenoid valves controlling water flow or all the circulators in the water circuits.
Switch applied logic circuits in machine controls, say Guard open = machine stops but a keyswitched relay allows running during tool setting. Largely displaced by PLC controllers and ICs.
Mechanically, a relay would just take a switched signal current and use it to energise a coil on a solenoid or a motor to operate another switch.
Alan