Whenever you edit a style all the text in your project formatted with the style is updated automatically and immediately. In addition to this any changes you make to styles will automatically be inherited by any other styles based on that style. This makes it possible to make changes to entire families of styles very quickly and easily by editing the parent styles. For example, you can normally change the base font in your entire document by changing the font of the Normal style.
If the styles in the Edit Styles screen are read-only your project is using a Style Repository and you need to edit the styles there. See here for instructions.
If you manage multiple projects that all need to look the same, check out Help+Manual's powerful style repositories. They allow you to share stylesheets between multiple projects and edit the styles for all of them in the same central location. See the Working with Style Repositories chapter for details!