Quicklime is a stone-derived product used in the production of parchment.
Quicklime can be produced at a kiln or magma kiln by cooking any of the calcium carbonate stones (calcite, chalk, limestone, or marble). A dwarf must have the furnace operator labor active to do this. If you're using a standard kiln the process will consume one unit of fuel, and in either case you'll need an empty bag to store the finished product.
On its own, a bag of quicklime has no practical use. However, it can be further processed at an ashery into milk of lime, which is a crucial ingredient in the production of parchment. Much like certain other entertaining real-world materials, in-game quicklime does not pose any health hazard to your dwarfs and can't be weaponized for its Fun reaction with water.
Quicklime is stored under "Boxes and Bags" in furniture stockpiles, which makes it difficult to separate from empty bags. One workaround is to set up a kiln dedicated to producing quicklime and a furniture stockpile set to take only from that kiln. Quicklime produced at this kiln will then be accepted only by the aforementioned stockpile, which can in turn serve as a feeder stockpile for your milk of lime ashery. This approach will not remove existing quicklime bags from circulation among your other "Boxes and Bags" stockpiles, and purchased quicklime will not be accepted there.
Quicklime (also known as burnt lime or calcium oxide) is a caustic, alkaline crystal that forms a fine white powder. While its use in Dwarf Fortress is very limited, in reality it is a common industrial product, with usage dating back to ancient times in roles as varied as production of plaster for homes to use as a primitive chemical weapon.