Contactors and relays are used to switch greater currents than a standard switch would handle.
This can have a cost benefit, as the cabeling and control gear for the low current switching would in many cases be cheaper than cabeling and control gear designed to handle the larger current.
With the starter motor on a car for instance low current is switched via the ignition to a relay which then switches a large current to from the battery to the starter.
If a relay was not used, extra large diameter cable would have to be run from the battery to the ignition switch and then to the starter, and the ignition switch would have to be designed to handle the extra current.
The most common use of contactors is to switch currents used to stat and run motors.
However they are often used where there are lots of lights and where the lights are on different phases.
A single single phase switch is used to switch a 3phase contactor, rather than having a 3phase switch, or three single phase switches.
This also saves on cabeling, as only a single phase needs to be wired to the switch rather than wiring three individual phase conductors.