Morphological analysis attempts to model the rules that govern the internal structure of words in a language. For example, speakers of English realise that the words "dog" and "dogs" are related, that "dogs" is to "dog" as "cats" is to "cat". The rules understood by the speaker reflect specific patterns and regularities in the way in which words are formed from smaller units and how those smaller units interact.
Another way to understand it is splitting a source language word into its lemma and grammatical info.
- cats -> cat<n><pl>
- dog -> dog<n><sg>