The privilege awarded for reaching 250 reputation is called "View Close Votes". As explained at length on the privileges page, this means that you can view and cast votes on your own questions.
However, when you receive the notification in your profile page that you have earned the privilege, it simply says that you can now view close votes, but it does not say that you can only view votes on your own questions, as can be seen in this screenshot:
This can be very misleading, especially to a new user who has never seen this privilege explanation on the actual privileges page.
I think that the text of the notification should be changed to include "on your own questions".
Here are several other questions that discuss other confusing aspects of this privilege, but as far as I can tell none of them mention this particular misleading text: