Repos are short for "Repositories". They are collections of apps (and in the future audio/books/movies/etc). Adding/enabling a different repository allows you to get access to more than just the default list of apps maintained by the f-droid.org project.
The default repos you see when you install F-Droid are:
F-Droid (enabled by default): The list of approximately 2000 free and open source apps built from source and distributed by the F-Droid project.
F-Droid Archive: Same as F-Droid, but the main repo only includes the 3 most recent versions of any single app. The archive includes up to 8 (from memory). Separating them like this means the main repo doesn't take as long to download.
Guardian Project: The Guardian Project make privacy-focused apps. They have been collaborating with F-Droid to help develop and fund the project. Note that this is not why they are a default repo. We'd also be more than happy to add other default repos if, for example, VLC or Mozilla were to host their own repo containing their apps.
Guardian Project Archive: See F-Droid Archive above.
There are a number of 3rd party repos, some of which are documented on the wiki. In addition, anyone is free to maintain their own repository of apps for others to use also. We are right in the middle of developing a new web-app to help make this really easy, and are looking to release it over the coming months, so make sure to hang around
In the future, we are considering renaming them to something like "Collections", but haven't made up our mind on the exact terminology yet.