See also the official documentation:
Help Center > Members Manual > Working with files > Uploading files and folders

Bulk File Upload

How to Do It: 

1. Select "Files" on the left-side menu, browse through the existing directory structure, and select where you want the files to go.
2. Click on the blue "Upload File" button at the top of the page.
3. In the resulting Upload File dialog, click the Browse button.
4. Select as many files as you want from the resulting File Explorer "Open" window. In Windows, you can do this by clicking and dragging with the mouse, or hold down the CTRL key while clicking on several files.  If there are several contiguous files, select the first, hold Shift, and select the last.  CTRL-A will also work to select all the files, but you have to click somewhere in the "Open" box first.
5. When you're done making your selections, click the Open button at the bottom.
6. The files you selected should now appear as thumbnails in the Upload dialog. Some of these thumbnails may not render properly, and could even display an error message. Don't worry about this, it's not important (e.g.: https://groups.io/g/GroupManagersForum/topic/25431767#11702).
7. Enter a description if you want and click the blue Add button to actually upload them.

Note:  You may have noticed that if you select a folder, the folder will not appear among the thumbnails in the Upload dialog. There is no provision within groups.io to upload a folder and its contents in one step. You have to manually create the directory structure within groups.io first, using a series of "New Folder" operations. At that point you can then upload a collection of files into each folder.