Relays are the components that physically cycle the elements on and off to your kiln. If the kiln is firing too fast or too hot the controller will tell the relays to turn off and if it is firing too slow or too cool the controller will tell the relays to turn on.
Most kilns will have at least two relays. Relays have a limited life that is determined by the number of times they cycle on and off. Excessive heat can shorten the life of relays so make sure your kiln room is well ventilated.
There are many different types of relays. The most popular are mechanical relays. When they fail they can fail in the on or off position. If they fail in the off position the elements they control will not receive power which will most likely trigger an error code by your controller and shut down the firing.
If the relays fail in the on position the kiln will often complete the program but may never completely cool. If your relays fail in the on position turn off the breaker to your kiln and unplug it from the receptacle.
The likely of more than one relay failing in the on position at the same time is very slim therefore the risk of losing ware or damaging your kiln is slim. Most kilns divide the power between 2 or more relays so if one sticks it will not over fire the kiln.
It is very important that you use only manufacturer recommended relays for your particular model when replacing them. The relays are located inside the control box. If you choose to replace them yourself it is very important that you disconnect the kiln from the power source first.