Since a cone measures the absorption of heat over time ceramic artists use it to determine when a piece of set of pieces is finished firing. All pottery products including clays and glazes tell the cone number that their products should be fired to. The artist puts that cone in the kiln and watches for it to bend. When the cone bends the firing is finished and the product should be complete and fired correctly.
The three cone method is a way of assuring that a piece of pottery gets fired to the correct temperature level. When you fire with the three cone method you need three different temperature cones. The first is the cone number that the manufacturer recommends. You also need the cone number that is one above and one below that number. For example, if your piece gets fired at cone number three, you place cones two, three and four in the kiln. Your piece is finished when cone two is over-fired, cone three is correctly fired and cone two is under-fired.
You can also use cones to monitor the temperature in your kiln. Sometimes kilns have warmer or cooler spots just like conventional ovens. If your kiln is warmer at the top or bottom then pieces in those areas will fire more quickly than pieces in the center of the kiln. Placing identical cones on the top, center and bottom shelves of your kiln and checking them after firing will help you to identify any warmer or cooler spots and to adjust your methods accordingly.
Cones can help you to detect possible issues with your kiln. It is common to use one cone for most firings and occasionally use the three cone method to check the performance of the kiln. If you save and label cones from previous firings you can tell if your kiln is heating consistently or if there is any temperature variation. More than a half cone variation in temperature between different test cones is a sign that you may need to change how you load or run your kiln.