Distill has browser (Chrome, Opera, Firefox) extension and the Web App (distill.io/login). Monitors which you add using browser extension run (checked for changes) on your local computer and so are called local monitors. For local monitors to run for check for changes, your browser should be open. Similarly, monitors you add through cloud/Web app (distill.io/login) are cloud monitors. These cloud monitors are stored and are run in cloud. You do not need your computer to be open for the monitors to run in case of cloud monitors.
When sync is enabled for your account, you can view all your monitors from any of the extension or apps, irrespective of device the monitor is running on. You can also change the run device for the monitor. In the following image, sync is enabled and it shows all monitors in one account being run in Chrome, Firefox and Web app:
In the above image, 3 monitors are running on the current device (computer icon), 1 in Web app (cloud icon) , 1 in Firefox and 1 in other Chrome device. You will receive audio and pop-up notifications only for the monitors running in the current device.