A contactor is an over-sized, heavy duty relay. It serves as a mechanical / physical break in the circuit. SSRs have a tendancy to leak voltage, fail in the closed position, and otherwise do whatever they want. So even though your PID may show that it's not triggering the SSR, it's still possible that the SSR is sending some current to the heating element. This can be problematic if you are cleaning your kettle, or even just from a dry-fire perspective. The contactor uses a small input voltage / amperage (you can get a variety of ratings) to close a terminal block that controls the main power source. This way you mount the contactor to your back plate and run all your heavy gauge wires to it, and then put a small switch on your panel door, and run small easy to manage wires to the contactor. Push the button on the panel, the contactor closes, the circuit is complete, and everything works. Push it again, the contactor loses the input voltage, it opens, and the circuit between your PID - SSR - Heating Element is broken and no power will go to the element.
It's basically a substitute for a big 30 amp rated switch mounted to the front of the panel - easier wire runs, better looking switches, and it keeps all the heavy gauge wire to the back of the panel and not on the front.
-Kevin