|This article is about the current version of DF.|
The alchemist skill does not currently have any use in Dwarf Fortress. It was originally included in the game alongside the alchemist's laboratory for making soap, a function that has now been taken over by the dedicated soaper. The alchemist skill and alchemy labor have not served any function since version 0.28.181.39a and have been removed from the visible game, but Toady One has shared some thoughts regarding its use with reactions in a future version of the game; for now, though, the skill is likely to languish in the background.
There also once existed an alchemist noble who would arrive at the fortress after ten relevant jobs: either making soap or extracting essences from plants, vermin, or fish. He had light furniture requirements, could issue demands, liked working in the alchemist's laboratory, and was phased out at the same time less lofty alchemists were.
In the real world, alchemy is a primitive precursor to chemistry, mingling some legitimate material science with a great deal of occultism. Alchemists were preoccupied with, among other things, transmuting metals, creating universal panaceas and solvents, and searching for the elixir vitae that would grant them immortality. More practically, real-world alchemists discovered phosphorus, perfected distillation, researched smelting techniques, experimented with extracts, created new medicines, and identified or discovered a wide assortment of acids, salts, and other useful compounds. Some of these basic alchemical processes or products are already present in Dwarf Fortress to various degrees, but the individual functions fall under different skillsets.
Alchemy as implemented in the game could possibly have to do with extracts and reactions and the creation of healing medicines and military-usable poisons. Transmutation is also possible, but is probably unlikely. Researching new materials and material applications is also a possibility.