What happens after you grant accessibility permissions to an app downloaded from the Mac App Store (Accessibility Permission = Control Over Your Mac) I recently installed an app from the mac app store known as commander  one from the mac app store which allows you to transfer files between the Cloud, Mobile devices and your mac, but as soon as I installed and opened it, it is constantly asking for accessibility permissions in - order to control my mac, so I deny it every-time it asks for it, so can anyone tell me why the app asks for this permission and what it would be able to do after granting this permission?
Controlling your computer means that software can type for you and make changes to your settings, copy data off the clipboard (think passwords and social security numbers if you ever copy / type them) and generally get at things without you having to type or move the mouse. 

Apple put that question there for you to say no always unless and until you really understand how that access is to be used and hopefully you have appropriate trust with the app developer in question. 

The same NO should go with typing your password as an administrator when you install software or it asks to do things as root. The percentage of apps that truly need a kernel extension, admin permissions, control over your keyboard and mouse is far less than ask for it.

Once you give control of the both the UI and admin credentials, that Commander One software could then do whatever it pleases with your files and data and system until you remove or revoke the grants of elevated permission. 

I’m certainly not saying Commander One does any of that - just that is asks for all the capabilities and nothing would stop that program if it were programmed to do such things.