Anyway, today while trying to update some apps I kept getting "insufficient space" error messages. So I tried to uninstall a lot of apps I didn't recognise or knew I'd never use. A lot of them seem to be core apps and can't be uninstalled. Why a pinball game has to be core, search me. Uninstalling updates did free up a bit of room.
One app that can't be uninstalled is the one in the following picture.

(Edit: The phone is running Android 2.3.5 - coincidence?)
It's got the following permissions.
Your personal information: read contact data, write contact data
Network communication: full Internet access
Your accounts: contacts data in Google accounts, Google mail, use the authentication credentials of an account
Storage: modify/delete SD card contents
Phone calls: read phone state and memory
System tools: modify global system settings, prevent phone from sleeping, write subscribed feeds
So many apps seem to have such extensive permissions that I don't know whether the above are OK, dangerous or uninterpretable.
Can anyone explain this mystery app to me? Thank you in advance.