This dance/game is actually called Kikli and Kaleer means a little girl. And since the first two lines of the song almost always go as Kikli Kaleer di, Pag mere veer di (Kikli is dance for little girls, and the turban is for my brother), the dance/game/song is commonly known as kikli kaleer di.
Here in the song from Luv Shuv tey Chicken Khurana, the traditional song is changed to Kikli kaleer di, hatt gayi heer di, ranjha kare cheat ji, kare heer kya, saying that when Ranjha cheats on love of his life Heer, what should Heer do.
Basically the words are used for two reasons, one, the words Kikli kaleer di are not just popular, they give a traditional and catchy music base to the song, and secondly, it also completes the motive of the girl in the song trying to keep thing traditional and normal, but the guy wants to change that and hence the girl complains by making change in the song.
[Photo courtesy: punjabigraphics.com]