It would appear that the leader of the Klingon High Council likes to say the word Titten (In German means Boobs, I think). Robert O'Reilly has played the character for almost ten years on both TNG and DS9, until Worf killed him in the last few episodes of DS9. And, those rather large eyes are actually real and not part of the makeup.
This clip I believe comes from the CD videogame Star Trek: Klingon (Think Star Trek: Borg, but with Klingons.)
Someone liked Gowron so much that they made a dance number out of his 'titten'.