Pressing the button will open the Active File Drawer. Here you can view every currently open file. Tapping on a file will return you to that file and tapping the little x on the thumbnail will close that file. A file you have edited but not saved, will have a red dot instead of an x.
As of version 7.0.5, the Access iOS mobile app can unzip archives and 8.1 and newer can also create them. These features are controlled by your Files Advanced and you may not be allowed to use them.
Unzipping an archive
Note: Unarchived data will be downloaded from the server to your My Files folder that resides on the device.
Archiving files
Available in <PRODUCT_NAME 8.1 and newer.
Note: If you do not have write permissions, the archive you create will be saved locally in My Files.