A repository is a special uncompressed Help & Manual project that you use to share styles and snippets between multiple projects. They are quite specialized and you should really only use them if you have multiple projects that must all have exactly the same styles. This is an excellent way to ensure that your styles are standardized for everyone when you are working on a project in a team, for example.
Ideally, you should edit the styles for all the projects in the 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 Repositories is only included in the Professional and Server versions of Help & Manual. Repositories are not available in the Basic version.
A 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.
In addition to this, it 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 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.