The Skeksis are the political rulers and live in the Castle of the Dark Crystal. The Skeksis are the evil side of the urSkeks and will stop at nothing to keep their power and live forever. In an attempt to make this dream come true the Skeksis tried to stop the prophecy of the healing of the Dark Crystal by killing all Gelphling. Fortunately, they Jen and Kira survived.
In this scene, the Skeksis are gathering before the Dark Crystal for the Great Conjunction during which, if the Crystal is not healed, they will get to live forever.