A morpheme refers to units of meaning, and they range from whole words to a single letter. The word dog is a morpheme because all three letters are necessary, in that order, to reference a canine. A plural -s (or -es) is also a morpheme, since it changes the meaning from one dog to multiple dogs.
Studying morphemes—the field of morphology—helps readers mentally break words into syllables for quicker and more accurate reading. Morphemes can also help identify a word's part of speech, punctuation, and definition. The morphemes -ing and -ed, for instance, usually signal tense; thus, the root to which these are affixed is usually a verb. In the same vein, the morpheme -ly typically signifies an adverb.
By learning Latin and Greek prefixes, suffixes, and root words (which are all morphemes), readers glean tips for pronunciation (ph = f; tion = shun) and meaning (ject = throw; mob = move; re = again, etc.) Thus when confronted with an unfamiliar word—such as expulsion—they can figure it out. The morpheme ex- means out, the root puls means to drive, force, or push, and the prefix -sion (or -ion) signals a state or condition. So, expulsion means the state of being forced out of something. Even when readers can't determine the exact definition of a word, morphology can help them make an educated guess. For example, the prefix un- means not, so the meaning will be opposite to the meaning of the root. The root hydro(a) means water, so words with this root will have something to do with H2O.
Knowledge of morphemes can help spelling too. A good example of this is the suffix -ed. It signals past tense, but it's pronounced three different ways (compare stopped, grabbed, and added). A writer needs to know that when spelling, say, talked, it requires an -ed even though it sounds like a /t/.