A morpheme is the smallest distinctive unit of meaning in English. Morphemes are concepts. In both spoken and written English, they can have varying physical representations or realizations, which are called allomorphs. A written realization of a morpheme is called an element.
Elements include bases (such as <slip, do, quest, struct, hap>) which are the main nuggets of meaning in words, prefixes (<in, de, pre>), suffixes (<ion, ure, ing, ed>) and connecting vowel letters.
For more detail on morphemes, including free and bound bases, read Terminology: Morphemes and Morphology.