The Forward says the following about the origin of the Mezinke Dance aka Broom Dance (link):
The mezinke tanz, or krenzel, is a special dance done by Ashkenazi Jews at a wedding to honor parents who have just married off their last child. The krenzel, or crown, is the wreath of flowers traditionally placed on the mother’s head during the dance. The parents sit on chairs in the middle of the dance floor, as friends and family dance around them in a circle, with each person kissing them as they pass...And the Philogos from a few years ago (link):
According to Hankus Netsky, founder of the Klezmer Conservatory Band and professor of Jewish music at the New England Conservatory, the dance is a Ukrainian custom, brought to America by Ukrainian Jews. Mezinke literally means “youngest daughter” in Yiddish. For Americans, who are a more egalitarian sort, it became custom to do the mezinke for the last child who is “married off.”
As is true of Mr. Zimilover, many people who do not know Yiddish know the word mezinke from the song “Di Mezinke Oysgegebn,” which is, among Ashkenazi Jews, a favorite at weddings and a must at the wedding of a youngest daughter. Often this song is accompanied by a dance known as the mezinke tantz, in which the parents of the bride sit in the center of a circle and the wedding guests dance around them with brooms. The explanation commonly given for this custom is that the brooms symbolize the “sweeping out” of the last unmarried daughter in the family, and while it sounds suspiciously ex post facto to me, I can’t think of a better one. In traditional Jewish homes it was once taken for granted that daughters were married in the order of their ages, and any parent of girls knows — may the spirit of feminism forgive me — that, far more than in the case of sons, it is a relief from worry when the last daughter has found a mate...
And yet there is one puzzling thing about this, which is that while the mezinke tantz is said to be a traditional one, the lyrics and music of “Di Mezinke Oysgegebn” were written in the second half of the 19th century by the songwriter Mark Varshavsky, who also composed the much-beloved “Oyfn Pripetshik.” Is the dance not as old as it is thought to be? Or was it (as is more likely) performed to different music before “Di Mezinke Oysgegebn” was written? I would be curious to know.