Morphology is the study of forms of words. Morphemes are the smallest units of meaning within words. That dinky little s at the end of the word dogs is a morpheme because it demonstrates that there is more than one dog. It does not simply represent the sound /s/. That s holds meaning. Words can, literally, morph into other forms with the addition (or deletion) of letters and letter combinations that hold meaning.
In the word sing, that i-n-g is just--part of the word. Sing is a free morpheme because it holds meaning standing on its own. On Your Way with Dr. Christina Williams