The primary purpose of a style repository is to have a common source of styles for multiple projects. It makes it possible for you to edit the styles of multiple projects in a single location. You can also share snippets with a style repository, but the styles are the "glue" that the repository uses to keep your projects synchronized.
In a nutshell: You can use style repositories to import styles to your projects and to share styles with multiple projects so that you are sure that you are using the same styles in all your related projects. You can also lock repository styles so that all team members working on a project can only use the predefined styles, because the styles can only be edited in the style repository project.