A morpheme is the smallest unit of meaning in a language. The study of morphemes is called morphology.
For example, the word "dogs" includes the morpheme "dog" (conveying lexical meaning) and the morpheme "-s" (indicating number). The morpheme "dog" is called a free morpheme, as it can be used as a separate word; the morpheme "-s" is called a bound morpheme, as it cannot. Bound morphemes include affixes and clitics.