Paragraph and character styles are presets for the paragraph and character palettes, respectively. Paragraph Styles contain some character properties, though, for the purpose of not requiring two presets when you just need one.
To create a new style, go to either the Paragraph or Character Styles palette, and click the New button
. A new Paragraph or Character Style will be created with the current paragraph and character settings. To modify it, double-click it. To delete it, click the delete button
.
Even though it's not as prominent, Microsoft Word also uses paragraph and character styles. When you place text from Word, you will get a new Paragraph Style that is usually called "Normal" that results from placing a Word document. Feel free to delete it. The only reason it's there is to perfectly preserve how the Word document looks from Word to InDesign.