Fermentation is the operation in which the alchemists were closest to a process the modern world understands completely, and furthest from understanding it themselves.
What the word describes
Fermentatio means the change a substance undergoes when a small quantity of an active material is added to a larger inert mass and the whole is left in gentle warmth. Bread, wine and beer were the everyday models, and the sources use them constantly. Closely related in the literature is putrefactio, the rotting that precedes the change, which some authors treat as a separate operation and some as the same one under another name.
That a pinch of leaven can transform a whole vessel was, before microbiology, one of the most genuinely astonishing observable facts available, and the alchemical use of it as a model for transmutation is a reasonable inference from what could be seen.
Where the number seven comes from
A numbered sequence of exactly seven operations tied to the seven planets is a modern arrangement. Historical treatises vary: Ripley's fifteenth-century Compound of Alchymy has twelve gates, and fermentation and putrefaction appear as separate items in some lists and as one in others.
The atlas records the seven-step scheme as the version in general circulation and records here that it smooths over a real disagreement in the sources.