If a product class has a considerable amount of attributes, it makes sense to divide them into groups to make the representation for a customer structured and easy to perceive.
To add a group of attributes to a product class:
In the list of product classes, locate the product class that you need to add an attribute to, and click on the "Edit attributes (N)" link opposite it:
A page where you will be able to manage attributes for this product class will open:
On this page, click "Manage Groups."
A popup titled "Manage attribute groups" appears.
Use the "New group" button to add as many attribute groups as you need:
Click the "Save changes" button when you are done:
The newly created groups will add to the product class details page:
Now you can use these groups when creating attributes for this product class.
The further maintenance of the attribute groups is performed through the "Manage groups" popup:
Here you can:
re-arrange groups using the cross icons for drag-n-dropping;
delete groups using the respective trash icon (the attributes assigned to this group will not be deleted but moved to a "No group" section);
add new groups to the list.