Character styles are styles that apply to individual letters and words rather than to entire paragraphs. Character styles are very powerful (and somewhat dangerous) because they can override paragraph styles. For example, you can use character styles to changing the font weight of a few words inside of a paragraph.
Character styles can be used for three purposes. First, they can be used to define a style change within an existing paragraph. For example, if you want a couple of words in a paragraph to be bold, without the rest of the paragraph being bold, you can select the words you want bold, then click Styles, Strong Emphasis in the top menu of Libre Writer. Note that this is different from Direct Formatting where you would select a few words and then click on the BOLD icon in your formatting toolbar.
The second purpose of character styles is to define any styles that you want to remain after clicking Format, Clear Direct Formatting in the top menu. If you click on the Bold Icon in your formatting toolbar, that formatting will be eliminated after clicking Clear Direct Formatting. But if you click on Styles, Strong Emphasis, the bold text will remain and not be changed back to normal text.