Morpheme

Morphemes are sounds that have a meaning. Morphemes are the building blocks of words.

A word is made from 1 or more morpheme.

Example
In this example, teaching is 1 word, which is made by adding together 2 morphemes: teach + -ing.
 * e.g. teach + -ing = teaching

The root teach has the main meaning of the word.

The suffix -ing also has a meaning. It adds some grammatical information (progressive ASPECT) to the root word, which makes it possible for us to understand that the action of teaching is not complete, instead it is still in-progress.

Types
You get 2 types of morphemes:

English and Other Languages
In English the root of a word is often an independent word.

In some languages, this is not true, and the root of a word cannot exist as an independent word (e.g. Latin, Italian).