There is an app called smart app lock. It has an option to prevent uninstalling of the app. Ticking it gives confirmation to add app to system administrators.
Root was not required to make it work. What privileges does this 'Administrator' get? I know that root has more privileges as I could uninstall it with root privileges, but what is the difference between the privileges of admin and those of root?
Device Administrators are apps which the user grants certain privileges. For example:
And some other options, including the possibility to prevent uninstalling of the app.
So the difference is that with root you gain the possibility to modify the system at all levels, instead with administrator you can gain control over a limited set of options - which are of course available to root.
Another difference is that administrator permissions are built-in in stock Android and available to apps developer through the dedicated API. You can see which permissions are granted to which apps and revoke them by going to Settings -> Security -> Device administrators.
A device administrator, when talking about an app, is basically an app which had extra privileges over other non-administrator apps. These "administrator" privileges do not require root access and only give the app certain extra functionality.
An app with root access is different and on a much higher and more dangerous level system-control wise. An app with root permissions can essentially do anything to your phone - delete virtually any file, secretly route your traffic to somewhere else, access things it otherwise wouldn't have access to.
However, that's not really a fair justification of what rooting can give you as it also provides benefits too, however this isn't really related to the question.
Rooting a device (to gain root privileges and to give an app root access) requires a process which usually voids a device's warranty, whereas for an app to become an app administrator you just need to enable it in your settings. A similar procedure is required for apps to request root access. However, while a device administrator can be enabled by tapping a switch and confirming a dialog, root access is usually presented to the user as a popup dialog with a timeout.
Also, the (main and most probable) reason why your app locker app requests to become a device administrator is because device administrators cannot be uninstalled without you first disabling them (this process is basically the same as enabling it, however without the confirmation dialog). This is because someone who might want to access an app which you have locked might just uninstall the app locker to access it - this adds some security in that they have to spend the (albeit small) amount of time disabling it, and if they don't know how to (as this isn't something you do every day, even though it is simple) it helps prevent them gaining access to apps you don't want them to.
