Both kindling and extinguishing a fire on Shabbat are considered forbidden activities for which a sin offering will be brought if it was done without realizing that it was Shabbat.
One who stokes coals on is liable to bring a sin offering. Rabbi Shimon ben Elazar says in the name of Rabbi Eliezer son of Rabbi Tzadok: He is liable to bring two sin offerings, because he extinguished the upper coals and kindled the lower ones. How is this case to be understood? If he intended to extinguish as well as to kindle, what is the reason of the one who exempts him from the second offering? And if he did not intend to kindle, what is the reason of the one who holds him liable for two? — Rabbi Elazar and Rabbi Ḥanina both explained the case as follows: The is referring to a case where a blacksmith needed the coals on top and he therefore intended to extinguish the upper coals knowing that this would set the lower ones ablaze. The first Tanna holds that one who produces an undesired or destructive outcome when he performs the labor of kindling is exempt; while Rabbi Eliezer son of Rabbi Tzadok holds him liable.
Why is it to the blacksmith’s advantage to extinguish the burning coals?
In order for the blacksmith to properly fire-up his forge to exceedingly high temperatures so that he will be able to soften the metal implements that he will hammer into shape. From ancient times, one of the popular fuels used to heat the forge was charcoal. Charcoal is obtained by heating wood until its complete pyrolysis (carbonization) occurs, leaving only carbon and inorganic ash. In many parts of the world, charcoal is still produced semi-industrially, by burning a pile of wood that has been mostly covered with mud or bricks. The heat generated by burning part of the wood and the volatile byproducts pyrolyzes the rest of the pile. The limited supply of oxygen prevents the charcoal from burning. The charcoal that is produced will burn at twice the heat of ordinary wood, with almost no smoke or smell.
In our case, apparently the larger pieces of wood were on the top and the blacksmith wanted to extinguish them to use as charcoal, while he had no interest in the smaller pieces at the bottom.