A morpheme is a minimal linguistic unit that has a form as well as a function or some semantic basis (basically, a meaning). Let me explain this linguistic terminology. Traditionally, it was thought that “words” were the smallest structural and functional units of any language. But it was soon realized that even words could be broken up further into meaningful parts. And these parts into which words could be further broken down were called morphemes (Just to add, the study of internal structure of words or morphemes is called morphology).
To have a better understanding of morphemes, we will have to examine some words (well, linguistics is less theory and more field work!). For our purpose words like- “boys”, “finished”, “going”, “normally” and “capitalization” will be of good help. Although at first it looks like these words are single units, a careful observation will reveal a different picture.
The word “boys” = boy + -s
So the word “boys” has 2 morphemes, i.e. boy and -s
In this case, “boy” is a lexical item with a clear meaning that we all know. It falls under the grammatical category of noun. The second morpheme, i.e. –s also has a meaning. Any native speaker of English will easily tell you that –s is a plural marker or, in simple words, has a function of making singular nouns into plural.
Note that the two linguistic items (boy and -s) cannot be further broken down (smallest units) and have a function or meaning associated with them. So they are called as morphemes.
Finished= finish + -ed
(Here –ed morpheme is the past tense marker)
Going= go + -ing
(Here, -ing is the progressive tense marker)
Normally= normal + -ly
(The morpheme –ly makes adverbs from adjectives and adjectives from nouns)
Capitalization= capital + -ize + tion
(The morpheme –ize makes a noun into verb and the morpheme –tion makes verb into noun).
There are two types of morphemes, i.e. free morphemes and bound morphemes.
In the above examples, morphemes like “boy”, “finish”, “go”, “capital” are free morphemes, i.e. morphemes that can stand independently.
On the other hand, morphemes like –s, -ed, -ing, -ize, -tion, etc. cannot exist independently. They need another morpheme to express a meaning. They are called as bound morphemes.
One can also classify morphemes as roots and affixes (suffixes and prefixes). The morpheme containing core meaning of the word is called as the root of the word. The morphemes attached after or before this root become affixes. Note that there are certain rules for breaking up a word into constituent morphemes that sometimes needs an etymological study as well.
I also want to add that the concept of morphemes is actually quite a controversial one in linguistics. This is because, for example, there are certain morphemes that do not have a form but have a meaning (ablauts). There are other morphemes that have a form but no predictable meaning (like words from Latin and Greek are sometimes borrowed in English as it is and loose meaning in the process, for example- the morpheme “ceive” in words like “perceive”, “receive”, “deceive”, etc.). Different morphologists hold different viewpoints for such cases.