“A minimal unit of grammar into which a sentence or a word can be divided. E.g., come inside can be divided into the minimal units come, in- and –side; distasteful into dis-, taste, and –ful.
The term was introduced, originally in French, in the late 19th century, and its use in English reflects in part successive technical definitions from the 1930s and 1940s especially. Thus, in detail: 1. A “morpheme” was at first a unit within a word which has grammatical as opposed to lexical meaning; originally opposed in that sense to a “semanteme.” For Martinet, in the 1960s, it was thus one type of moneme. 2. In Bloomfield’s definition a morpheme is a form with either a grammatical or lexical meaning. It was thus one element in a minimal linguistic sign: e.g. the morphem dis in distasteful as linked to a meaning “not” or “negative.” It is on this use athe “moneme” was later modelled. 3. As defined by Charles F. Hockett and other Post-Bloomfieldians, it was an abstract unit at a grammatical level of representation realized by a form, or two or more alternative terms, at the level of pholology. These are its allomorphs, e.g. the [dis] of distasteful might be seen as one allomorph of a “negative” morpheme, of which another would be the [un] of unpleasant.
Sense 1 is effectively obsolete in English-speaking countries, where sense two tends to be more normal.”
Excerpted from: Matthews, P.H. The Oxford Concise Dictionary of Linguistics. New York: Oxford University Press, 2014.