Hi John
Firstly, note that this will change significantly when the current major update to Types is complete, which you can read about here: https://toolset.com/2017/09/first-beta-of-types-2-3-with-post-relationship/
Bearing in mind that the current implementation is based upon standard WordPress posts and post meta, stored in the standard wp_posts and wp_postmeta tables, the current situation is as follows:
Repeating fields mean you can have multiple instances of a field assigned to a single post, e.g. if you want to add a custom 'to-do' field to a 'project' post type you can add as many to-do's to that project as you like, and as many to-do's to other projects as you like, each to-do field stored as an entry in wp_postmeta for the corresponding project post.
Say you want to store some additional information about the to-do's, such as status, priority, and deadline.
You could add repeating fields for each of these to a project, but they wouldn't be associated with the to-do's in any way.
With repeating field groups you could have a group of fields, to-do's, status, priority, and deadline, that were associated with each other and connected to the project post, and you could add as many repetitions of these associated fields as you wanted to each project.
But. These are not directly supported in Types currently (this will be added in the new version).
You can simulate repeating field groups by making a child post type of projects which is a container for the group of fields, and you can then assign as many child posts to the project as required. So you might make a child post type called 'task' and this post type has custom fields for the to-do, status, priority, and deadline.
Under the hood this is still how repeating field groups will work in the future version, but the UI will be substantially improved and you won't have to deal with registering the child post type yourself.
If you go ahead and make a site based upon the above now, it will migrate to the new system automatically when available.
You can read more about post relationships here (https://toolset.com/documentation/beyond-the-basics/post-relationship-concepts/) and here (https://toolset.com/documentation/user-guides/creating-groups-of-repeating-fields-using-fields-tables/).