Actually “alla carbonara” means “"in the manner of the charcoal makers " (“Alla maniera dei carbonai”) and refers to a sauce for spaghetti containing eggs, minced bacon (‘pancetta’, in Italian) and grated cheese (especially "Pecorino", salty cheese, made out of sheep's milk).
This was in fact the original recipe which was popular among charcoal makers, i.e. the “carbonai” who prepared and maintained the charcoal pits or the charcoal piles, covered with earth and turfs, which converted wood into coal, after a small fire has been lighted in.
The “carbonai”, who existed until the 1950s in Toscana, Umbria and Lazio, were forced to live away from home for several months and then used to prepare simple dishes like “spaghetti alla carbonara”.