In response to this order, Pakistan Telecom began advertising a hijacked route for YouTube, which caused all internet traffic to YouTube from around the world to be blocked for several hours. Here is a full writeup of how this happened.

I found this great Slashdot comment that explains how to use BGPlay to see an animation of Pakistan Telecom re-routed YouTube for the world.

Here is how the net looked during the hijack. The red dot on the left is YouTube, and the red dot on the right is Pakistan Telecom:

After YouTube announced new routes, traffic returned to normal for those outside Pakistan:

The animation is pretty neat! Also, Wikipedia has a good summary of the Border Gateway Protocol, which is the protocol that routers use to talk to each other.