Of all the operations, distillation is the one where alchemy left the most durable mark on the world outside it.
What the word describes
Distillatio means heating a liquid until it vaporises, then cooling the vapour so that it condenses in a separate vessel, leaving behind whatever did not rise. Repeating the operation concentrates the volatile fraction further, which is why the texts insist on doing it again and again.
What it produced
The apparatus for this operation, the still and its cooled head, was developed and refined by alchemical practitioners over centuries, and the equipment and the technique passed directly into pharmacy, perfumery, the production of spirits and eventually into industrial chemistry. Concentrated mineral acids, which made most of early modern chemistry possible, are products of distillation practice.
Whatever is thought of the transmutational programme, this is a case where the laboratory work was straightforwardly productive and its results are still in use.
Where the number seven comes from
The scheme of exactly seven numbered operations matched to the seven planets is modern. The historical sources give varying counts; Ripley's fifteenth-century Compound of Alchymy sets out twelve gates, with sublimation and distillation as distinct items. The atlas records the seven-step scheme as the common modern arrangement and notes that it is one.