A pyrometric cone is a small shaped piece of ceramic material formulated to soften and bend at a known combination of temperature and time. That combination, heatwork, is what clay and glaze actually respond to, and it is not the same thing as the number on a controller.
Temperature is not heatwork
A body held at 1200 degrees for two hours matures further than the same body that touched 1220 for five minutes. Clay and glaze respond to the total heat received over time, and a cone integrates both because it is made of ceramic material that behaves like the ware. A thermocouple reports an instantaneous temperature at one point; the cone reports what the pots got.
How to read them
Cones are numbered, and each bends at a defined heatwork. Set three in a row: one below your target, one at it and one above. After the firing the first should be fully down, the target one bent to about four or five o'clock, and the third still standing. That tells you at a glance whether the firing was correct, short or over, which no single number does.
Where to put them
Somewhere you can see them if the kiln has a spyhole, and in the parts of the load you are least sure about, which usually means the bottom and the top. A cone that is down at the top and standing at the bottom is reporting a real temperature difference in your chamber and is telling you how to pack it better.
Why they stay relevant
They catch what a controller cannot: a thermocouple drifting with age, elements fading so a schedule takes longer, a dense load shielding a corner. All three produce firings that report correct and come out wrong, and a cone that disagrees with the controller is the first sign. They cost pennies and they are used in professional kilns for exactly this reason.
Questions people ask about pyrometric cones
What are pyrometric cones for?
They measure heatwork, the combination of temperature and time that clay and glaze actually respond to, rather than an instantaneous temperature.
How many cones should I use?
Three: one below the target, one at it and one above. Their positions after firing tell you whether the firing was short, correct or over.
Do I need cones if my kiln has a controller?
Yes. Cones catch thermocouple drift, fading elements and cold spots, all of which produce firings that report correct and come out wrong.