If your devices are running Android 4.1+ and have already been rooted, please refer to the following steps to complete the authorization.
1. Initiate Remote Control on Desktop client (Win/Mac)、Web Client, or AirMirror App.
2. Find the pop-up window on the devices you want to control, then click GRANT to complete the authorization.
Alternatively, you can open the Root App (like SuperSU) to grant AirDroid Personal permission manually.
How to avoid granting permission for AirDroid Personal every time after upgrading/ re-installing AirDroid Personal？
Go to Settings of the Root app (like SuperSU) and make the Re-authentication option un-checked.
If you have a problem rooting your device, try the non-rooted way here.