An attribute group (shown in catalog listing and product search) allows you to cluster similar attribute values together. For example, you may have an attribute called "color" where the attribute value(s) on a product may be "sky blue", "baby blue", "denim blue", "ice blue", etc.  You can create an attribute group "blue" and cluster all the various shades of blue into that group.  Then, when your catalog is browsed the web user may filter the catalog by the attribute group "blue" and they will see all of the items with any of the blue shades.