Backups can be important if you sell something by accident or if something goes wrong with your data. You wouldn't wanna lose all that progress.
Also if you want to move from one device to another, it's good to know where to find the data.
Merge Dragons doesn't have an automatic synchronizing at this point.
Use the cloud for your backups.
<if anyone knows where to find the actual files, feel free to fill in more info>
For Android, you can find the necessary files here:
or alternatively /storage/emulated/0/Android/data/com.gramgames.mergedragons/files/
(another alternative is to search for "mergedragon" or "gramgames" within the file browser)
Simply copy the entire /files/ folder to a computer or a different place on your device.
To reactivate your progress on another device, download the game, start it once and immediately close it again.
After that you can copy the files from the old device to the new one to the same folder mentioned above.
On the next start, you should have your progress back.