Tag Groups are like containers that contain tags. These groups have IDs, names and an order in which they appear in tag clouds and in menus.
Tag Groups are only available for taxonomies (tag types) for which they have been enabled. Some functions work only with flat (non-hierarchical) taxonomies, such as (post) tags or product tags. Hierarchical taxonomies such as categories are not fully supported.
The same tag can be assigned to one or more groups. Only if a tag is assigned to groups, you can use that combination of tag and group in a post.
All tags that have not (yet) been assigned to a group form a default group with the ID 0.