Morphemes are the smallest units of meaning in speech. The word “love” is a morpheme. To that morpheme, another morpheme, “-ing” can be added forming “loving,” a different word. To that, “-ly” can be added forming “lovingly,” still another word.  

They are not the same as syllables.  Syllables break up the speech into rhythmic units.  It is possible for a morpheme to have more than one syllable, as in “rhinoceros” /raɪ nɑs ɚ əs/ which is a single morpheme that has four syllables; and it is possible for a syllable to have more than one morpheme, as in “walked” /wɑkt/, which has the verb “walk” and the morpheme “-ed” reduced to ‘t.’

Morphemes that can stand on their own, such as “cat” are called free morphemes, and ones that need to be stuck to another morpheme such as “-ing” are called bound morphemes.  Morphemes can be bound to either the beginning or the end of a word.  We saw “-ed” and “-ing,” above, two morphemes that are bound to the end of words.  Some morphemes that are bound to the beginning are: “in” (visible/invisible), “inter-” (active/interactive), and “non” (issue/nonissue).  A complete list of English prefix morphemes can be found here. Sometimes two free morphemes are stuck together, and in “bookseller,” “bootblack,” or “football.”