In painting jargon, a medium is something you add to paint to change it's handling properties, drying time, gloss, transparency, or other characteristics. Here's the recipe for my current favorite general purpose oil painting medium.
Combine equal parts Canada balsam, black oil, and oil of spike. Warm just enough to allow the incredibly thick and sticky Canada balsam to go into suspension with the other ingredients. Shake before using. Mix a very small amount into your paint to make it brush out more easily, adhere better to the previous layer, and dry more quickly. Keep covered to limit evaporation (you can add a touch more spike if it gets too thick).
Canada balsam is a sap from fir trees. Balsams improve adhesion from one paint layer to another and impart a certain silky smooth quality to paint. Canada balsam is clearer and faster-drying than other balsams, such as Venice turpentine. It also costs a lot more.
Black oil is linseed oil cooked with litharge (lead monoxide). Black oil is faster drying and more slippery than linseed oil. Like many art materials, it's poisonous, so you need to be careful not to ingest it.
Oil of spike is an organic solvent like spirits of turpentine, except that it is more slippery and evaporates more slowly. It has a very strong and wonderful smell (and is much more commonly used in aromatherapy than painting), although my wife doesn't like it. It has a long history in oil painting; Leonardo probably used it for the initial dark washy underpainting in his "sfumato" technique.
N.B., you can get all of these specialty artist's ingredients from Studio Products.