If the total amount of data exceeds about 2 GB they'll break it up into multiple zip files.
Inside the zip file(s) is a folder per group, and inside those are zip files for each type of content (messages, photos and attachments, files, etc.).
It is fairly well organized, and the messages are delivered as one or more mbox files (split for size if more than about 10 MB). Those files can be loaded into Thunderbird or other email apps as folders of messages. They likely also can be imported by support@groups.io.
The other content though seems problematic. In my case most of the groups' files and photos were missing; the download didn't even include all of the content I had posted.
My download (from an alternate account) finally came in today. It was a zip file containing folders for the seven groups that account was a member of.
Unfortunately for Susan and my email address theory, and consistent with Gerald's logical assumption, those seven were all of the groups in that account's Manage My Groups, without regard to the selected Email for each.
The help file Carol cited (THANKS CAROL!) tells you how to find a program to open the various types of files.
https://help.yahoo.com/kb/groups/understand-data-downloaded-yahoo-groups-sln35066.html
At the outer most level is one or more zip files. Under Windows 10 you can simply navigate into the .zip file as if it were a folder. Other operating systems likely have similar capabilities.
In the zip file you'll find folders for each of your group memberships. The very long folder names are inconvenient, but the group name is at the end of the folder name. Inside each group's folder is a .zip file for each of areas of the group: files, links, messages, and photos_and_attachments.
Files and Photos are stored as ordinary files. You can use the extract function, or just drag-n-drop them, to bring them out of the .zip and into a regular folder.
For the messages you need an application that can read mbox format. As the help page says that includes Thunderbird, Outlook, Apple Mail and likely many others. If you're going to import or re-post the messages into a Groups.io group leave them in the mbox files, and see this page:
https://groups.io/g/GroupManagersForum/wiki/Moving-to-Groups.io