The announcement is rather nebulous, as is their way. TorrentFreak has a more detailed explanation: http://torrentfreak.com/pirate-bay-moves-to-the-cloud-become... It's pretty much what you'd expect, though: The web site is now running on VMs on two unnamed cloud providers, accessed through a load balancer. All traffic is still routed through servers they control. The cloud providers apparently don't know that they'r…
If you know the physical and network location of their routing boxes and you keep polling some (e.g. static) resource on their servers you can eliminate all cloud providers that are further away than the response time as being the hidden backend.
Let's say you narrow it down to 10 candidates and 5 of them experience some sort of network issue that gets reflected in the response times of TPB, you've now narrowed it to 5.
I wonder what they're doing to mitigate these sort of timing attacks meant to discover their hidden backend.