the device-administrator role gives an app elevated priviliges. Use this tag only if your question is about this role.
What is "Device Administrator"?
An app can register as "device administrator", which usually requires the users confirmation. As device administrator, the app gains elevated privileges: it can e.g. define password policies (forbid "swipe-to-unlock", set a minimum password strength, etc.), but also wipe your device on remote command.
This was introduced with Android 2.2, mainly for enterprise applications; so it is e.g. used by apps accessing Microsoft Exchange servers or other enterprise resources:
For example, the built-in Android Email application has leveraged the new APIs to improve Exchange support. Through the Email application, Exchange administrators can enforce password policies — including alphanumeric passwords or numeric PINs — across devices. Administrators can also remotely wipe (that is, restore factory defaults on) lost or stolen handsets. Exchange users can sync their email and calendar data.
Google's device manager e.g. uses this as well: to remotely locate your device, make it ring, set a new lock password, or even remotely wipe it.