Server room with a seismic isolation floor during an earthquake GIF

Means the servers are stable while the building is not.

Well it looks like the camera is mounted to the wall, which isn't isolated from the vibrations, so the servers look like they're the ones moving when it's actually just the camera.

It's called seismic base isolation and here's how it works:
Japanese demonstration:
https://youtu.be/eU5nFvfCGsE

UC San Diego full scale demonstration test using the 2007 Peruvian quake data:
https://youtu.be/kXadHl1_gmE

Chilean example of use:
https://youtu.be/V6pxxan8bDg