A meta field group contains 0-many many meta field definitions as well as 0-many many meta field groups.
The meta field groups can be found in the DAM Center → System tools → Metadata.
It is important to select the correct meta field group. Depending on the meta field group, a meta data field may be used in different contexts. A prime example of this is the "Keywords" meta fields. There is a "Keywords" meta data field in the meta data field group Asset → Images → IPTC and another "Keywords" meta data field in the group Asset → Shared → All asset types.
The IPTC (International Press Telecommunications Council) meta field is used to hold very specific keywords defined by the IPTC. As such a user cannot edit or add to any IPTC meta IPTC meta data fields. Such a meta data field is used exclusively for images.
The "All asset types" meta data field is extremely dynamic compared to the IPTC one: This meta data field may be applied to any asset and any keywords may be added or removed from this meta data field by any users with write-access.