When you look at this video, it is not clear what you are looking at or what is happening:

What you are looking at is a 728 ton ball that sits in a shaft atop the Taipei 101 skyscraper. It is moving because the video was taken during the China earthquake several weeks ago. Here’s a nice explanation of this kind of “tuned mass damper” uses to stabilize skyscrapers:

in action: a skyscraper’s amazing 728-ton stabilising ball

Usually these dampers handle wind vibrations, as described here:

From the video description:

Installed anti-wind tuned mass dampers on the 90th floor. To improve occupants’ comfort in strong wind conditions — particularly in hotel and office spaces — two mass dampers were installed on the ninetieth above ground floor. The mass dampers use sensors to detect any swaying of the building and connects with a computer controlled, 150-ton counterweight suspended within the equipment by wire rope. In this way, the swaying problem of building is kept in control.

See also: Tuned mass damper

Here’s a great explanation of the Taipei 101 vibration problem in wind: