Richard plays the piano while couples dance in that funny way they used to dance in the 1950s. It is actually quite charming.
This is a clip from The Girl Can't Help It. Richard is just beginning to build up his reputation as a rock icon.
Pat Boone's poppy, polished version of Richard's originally raucous song was a bigger commercial success than Richard's own recording. This was a source of bitterness for Richard and his fans, especially because Boone's popularity had racial connotations (he was more accessible to a "cross-over" audience because he was white).
Elvis also made a popular version of the song.
This is just one great sample of Richard's wacky, unpredictable, and incredibly rhythmic way of speaking to the press.