Don't confuse "style repositories" with the repositories used in version control systems!
A style repository is a special uncompressed Help+Manual project that you use to share stylesm snippets and to a certain extent also variables between multiple projects. This is an excellent way to ensure that your styles are standardized across multiple projects. It is also a good way to make sure that everyone uses the same standard formatting when you are working on a project in a team.
Ideally, you should edit the styles for all the projects in the style repository, not in the individual projects. So if you only have individual projects with their own styles it is really more practical to work without a repository.
Please note that support for style repositories is only included in the Professional and Server versions of Help+Manual. Style repositories are not available in the Basic version.
A style repository is quite similar to a normal uncompressed HMXP project. The main difference is that it does not have a table of contents, because you never publish a repository project directly. It is a storage place for the text and paragraph styles used in other projects, allowing you to share the same set of styles between multiple projects.
A style repository can also contain topic files, which are available as snippets to all the projects that are linked to the repository. Since the snippets use the styles in the style repository, and the repository styles are available in all the projects using the repository, the formatting of the snippets is always correct. You don't need to worry about having matching styles in your own project, because the styles are already there.
If you define variables in your style repository they will also appear in the projects to which the repository is linked. However, the values of the variables are not dynamically linked, even if the styles are. The values of the variables in your projects will NOT update when their values are changed in the repository.