You'll see many group objects across Krypted Platform, but the most important ones are general Groups. These are managed in the Admin Panel of your application, and form the building block for every other group.
Permissions are used by most features, and enable members of the group to view, edit, and interact with content. For example, users with a view guild permission might be able to view a particular guild.
Complicated permissions are usually outlined in the documentation of the package you're looking at, otherwise they should be straight forward. For example, if you want someone to be able to have full access applications, just type applications in the permission search bar and find "Can approve, reject, and view applications".
Extensions such as the Discord Connector and EVE Connector will have interactions with groups, generally just attaching a group to some type of parameters.