How to add capability to author role to assign custom taxonomy terms to a custom post type?

Yes. It is some kind of mapping. So now, when I register the custom taxonomy I pass it:

 $caps = array(
            'manage_terms'  => 'activate_plugins',
            'edit_terms'    => 'activate_plugins',
            'delete_terms'  => 'activate_plugins',
            'assign_terms'  => 'edit_posts'
        );

With this result authors can now assign terms. I am just using ‘activate_plugins’ because, by default, authors do not have this capability and so by the mapping they cannot manage terms. If I put edit_posts here then they can manage the terms and I don’t want that.

So, what this seems to be saying, is “for this custom taxonomy any role which has the edit_posts capability will be able to assign terms from this taxonomy to any post which the taxonomy is registered to”

While this actually seems to work it is still opaque to me what is going on. I would be interested in any further explanations.