Red controller on the right: A Skutt Kilnmaster. Blue controller to the left of it: An Orton Autofire. These controllers both attach to a thermocouple in the kiln so they know the temperature. Both are external to the kilns (but there is a big difference). The controllers monitor the temperature change as they turn the power on in bursts, changing the length and frequency of the bursts to control temperature rise. The KilnMaster controller is attached to the 220V power line and the kiln power line attaches to it (there are heavy duty electrical relays inside). The blue Autofire controller connects to the switching mechanism in the other kiln (built to receive it), thus no heavy duty relays are needed within it. The KilnMaster is more flexible since it can connect to any kiln, but it is also triple the price.
In ceramics kilns the firing schedule of a kiln is typically managed automatically by an electronic device called a kiln controller. These are especially common on electric kilns.
A test kiln is a must for all potters and small manufacturers, even serious hobbyists. Here is why.