Without getting too technical, here's a brief overview on how this works in Armadillo. Online backups of your data are performed using the “mysqldump” command, which outputs all the content in your database to a file, which Armadillo then compresses into a zip file for easy downloading.
This means that your hosting needs to allow PHP scripts to run the “mysqldump” command, which is usually done via the “exec” or “system” function which is built into PHP itself. There are, however, a limited number of hosting companies that turn off “exec” and “system” for PHP, in which case Armadillo cannot perform an online backup for you.
If you’re unable to make an online backup, I would suggest contacting your hosting provider to see if they allow the system commands described above. Most major hosting companies do allow this.