Medium is taken directly from Latin, where, stemming from the adjective medius, it meant “middle,” “center,” or “interval.” It preserves that meaning but also acquired the sense of “intermediate agent” or “communication channel.”
The primary connotation is now of a substance through which something else moves, whether in a scientific context or in terms of the form in which art is conveyed or content is delivered. (Medium is also used in the sense of conveyance for a person who supposedly channels messages from the spirit world.) As an adjective, medium refers to something between large and small.
The plural form of medium is media, and art made of multiple materials or content available in several forms is called multimedia. The journalism industry is referred to collectively as mass media, and conventional, corporate journalism is labeled, often pejoratively, mainstream media. The phrase “in media res,” taken directly from Latin, literally means “in the midst of things.”
Other words based on medius include mediate (meaning “arbitrate” or “negotiate”) and its noun forms mediator (meaning “negotiator”) and mediation (meaning “the act of negotiation”), as well as intermediate, meaning “someone in the middle,” whether in the context of communication or in terms of skills; it serves also as a verb (meaning “come between”) and an adjective (meaning “in the middle”). (Moderate has a meaning similar to mediate and looks related but is akin to the Latin word modus, meaning “measure.”) Other forms are intermediation and disintermediation.
Mediocre, meaning “ordinary” or inferior,” is related to medium; the original, neutral meaning was “halfway up a mountain,” and it only later acquired a disparaging connotation. (The second half of the word, meaning “jagged peak,” is cognate with acrid, which refers to a sharp smell or taste.) Medieval, referring to the middle of history, between ancient and modern times, is also cognate with medium.
Medial, an adjective meaning “in the middle,” and median, which serves as both an adjective and a noun, are also descended from medius. (Remedial, from remedy, is unrelated; the medial syllable in that word has the same etymology as the first part of medical and medicine.) Median originally had an anatomical connotation, referring to arteries, veins, and nerves; now, it refers mainly to an area between lanes of traffic, though it also has the mathematical sense of the middle number in a series.
Mean, the same word distilled in French, has the distinct meaning of “average”; the mean is derived by adding a series of numbers and dividing the sum by how many numbers there are. (In lay usage, it more informally refers to something intermediate or midway.) The senses of mean pertaining to definition or intention and to being cruel or stingy are unrelated, but means—as in “by any other means” (meaning “any other way”), “by means of” (meaning “through the use of”), or “by no means” (meaning “not at all”), as well as “a person of some means” (meaning “someone with material resources”) is ultimately derived from medius. (So are meantime and meanwhile.)
Another French word that pertains to the middle is milieu, meaning “environment” or “setting”; the second syllable, meaning “place,” is the same element seen in lieutenant and “in lieu of.” Moiety, though it means “half” or “part” rather than “middle,” is related as well.
Medium’s Germanic cognate, middle, also serves as both a noun and an adjective; another adjective, middling, refers to something of average or mediocre quality. Middle is used in various compounds such as middlebrow (referring to someone or something of merely moderate sophistication) and middleman (a go-between in a transaction).
Mid, originally a stand-along adjective meaning “among” or “with,” is loosely related to middle; it survives only as a prefix (as in mid-air) or as shortening of the preposition amid (amidst, in British English). Midst is also used sometimes in the latter sense, though it usually serves as a noun meaning “the middle part” or “the time while something is happening.”