The thermocouple is used to measure the temperature inside a kin. That information can be displayed and/or sent to a controller.
When any electrical conductor has a temperature gradient (one end is a different temperature than the other) it will generate a small amount of electricity. This principle is known as the thermoelectric (or Seebeck) effect.
Most modern thermocouples make use of conductive loops where each half of the loop is a different metal. The voltage is measured at the two spots where the metals meet -- one inside the kiln and the other outside. That voltage can be used to compute the difference between the temperature inside the kiln vs. outside the kiln (other electronics are used to read the actual baseline temperature outside the kiln).
Most kilns today use "type K" thermocouples that employ nickel-chromium and nickel-aluminum as the two metals. The thermocouples have approximate top temperatures of 2100°F (1200°C).