Attribute groups are not actually real attributes. They are used to group attributes that work together. You can use them to copy a set of attributes to several types. For example, you could create a group of two attributes: one value (for instance of type text or number) and a script to set this value. You will also be able to add an attribute to all these types later by adding another attribute to the group.
Attributes are added to a group by choosing Add Attribute from the attributes right-click context menu; they can be deleted from the group by choosing Remove Attribute. You can also copy existing attributes to a group by drag-and-drop in Rules.
Attribute groups are helpers for the Designer but they are never seen by the Developers.