A morpheme is formed by a collection of phonemes. There are two kinds of morphemes. Free morphemes, or roots, can stand alone. Bound morphemes, or affixes, need to be attached to another morpheme. Morphemes can be broken down into derivational morphemes and inflectional morphemes.
Derivational morphemes can form new words out of old ones.
Inflectional morphemes relate to grammatical categories such as plurality, tense, adverbs, comparatives, superlatives, and third person singular. The smallest unit that a word can be broken and still maintain meaning is a morpheme. Morphemes are the word structure for the language. Europeans usually express a single concept by one word, but a word in many other languages may express a number of ideas. Whenever new words are formed from existing morphemes you follow the rules of grammar, although there are exceptions.