How about looking at firing a kiln in more familiar terms: cooking.The principles are not that much different: just different parameters. Lets start with a meat thermometer: you use one to cook a piece a meat to a specific temperature. You stick the thermometer in the meat until it reads the desired temperature. Cones likewise measure a specific temperature, the only difference is you lay beside what your cooking: not in it. Which brings us to a kiln term: heat work. A thermometer measure the temperature inside the meat, not the air around it. A cone measure the heat that has been absorbed, not the air around it. Another way to view it: a fish fillet is broiled quickly at high heat, and yet it cooks through because it is thin. You subject a steak to that same cooking cycle and the outside will be seared, but the inside slightly cooked. Subject a roast to that same cooking cycle and the outside will be seared, but the inside will be blood raw- perhaps still cool. You control the oven to control the type of meat you are cooking- a kiln is no different. You lower the temperature of the oven so the heat reaches the center of the roast.
All the firing cycles you see in the Orton chart shows the results of a firing using low. medium, or high heat. (Degrees per hour). You start the firing lower to equalize the heat in all the pieces in the kiln. Once you have done that you can heat them faster, up until the end of the firing. Once you near the end of the firing, it is slowed back down to again equalize the heat in the entire kiln. The hardest thing to grasp is; its not the air temperature that determines if the clay and glaze is done cooking: it is the amount of heat that is transferred/absorbed by each piece.
So now we go back to the oven scenario: if you throw a couple of steaks in the oven you know they will absorb heat uniformly and you can cook them faster and use a higher heat. Now imagine you stuff your oven with 50 or 100 steaks? You have to lower the temperature and extend the cooking time to make sure they all cook evenly. So if you are firing a small kiln with just a few pieces: you can go faster. If you are firing a large kiln with many pieces, then you have to slow down. Clay and glaze are just like different cuts of meat: they require different cooking temperatures and times.