Normalization is the process by which you can perform certain transformations of text to make it reconcilable in a way, which it may not have been before. Let's say, you would like searching or sorting text, in this case you need to normalize that text to account for code points that should be represented as the same text.
The normalization is applicable when you need to convert characters with diacritical marks, change all letters case, decompose ligatures, or convert half-width katakana characters to full-width characters and so on..