A morpheme is a unit of language, but not necessarily a word.
A morpheme might be a word, or might be part of a word. It is "a small unit of language that contains meaning." A morpheme that is not a word would be an affix. An affix is a prefix or a suffix. A prefix appears at the beginning of a root word, and an affix appears at the end of a word.
An example of a morpheme is –ed. This is a suffix. If you put it on the root word talk, for example, it will become talked. It changes the meaning of the word. Yet –ed is not a wordby itself.
Consider the morpheme house. It can be part of a word, like doghouse. It can also be a small word by itself.