How does a PDF prevent itself from being printed?

The print permission is in the pdf file itself and is mostly used by Adobe products. Some products pay it attention, and some others print it anyway.
It is quite easy to remove.

See the article How To Unlock Adobe PDF Files, where it explains how to use Freeware PDF Unlocker to remove this and other passwords.

Warning : Comment by Chris Betti says

As of Oct 7, 2013, the Freeware PDF Unlocker setup installs unwanted software without confirmation, and fails to install the product itself.

Use older versions (if can be found) or search for another product.

It's part of the settings when you save the PDF. You can also disallow text to be copied. There are software that allow you to bypass the restrictions.