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.
If one removed coals from a burning pile on the Sabbath, he is liable to bring a
sin-offering; Rabbi Shimon ben Eli’ezer says in the name of Rabbi Eli’ezer son of Rabbi Zadok: He is liable to bring two 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 to two? — Rabbi Eli’ezer and Rabbi Hanina both explained the case as follows: He intended to extinguish the upper coals knowing that this would set the lower ones ablaze. The first Tanna holds that one is exempt for any kindling which is to his disadvantage; while Rabbi Eli’ezer son of Rabbi Zadok holds him liable.
In explanation of this case, Rabbi Yohanan clarifies that we are discussing the case of a blacksmith, whose intention is to extinguish the upper coals even as he lights the lower ones.
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.