Traditionally, this dance was performed at the wedding of the youngest daughter and it is danced towards the end of the wedding celebration (reception), usually before Birchat Hamazon and Sheva Brachot**. The Mezinke Tanz is meant to symbolize the "sweeping out or cleaning out the house" of all the unmarried children after the marriage of youngest daughter. It should be kept in mind that traditionally the daughters of a family were married off in order of their age and so the last daughter to be married off usually meant the parents no longer "had to worry about their children". Today the dance is performed during the wedding of the last child (son or daughter).
The song Di Mezinke Oysgegebn is traditionally played for the Mezinke Tanz. The lyrics and music were written by Mark Warshavsky (or Varshavsky).
There are several versions of this dance. In one version a broom or several brooms are decorated with flowers and the parents, holding these brooms, dance in front of the kallah and/or chatan, as if they were "sweeping them out of the house". In a version of the dance, as you can see in the following link (with the kind permission of David Wilder), http://www.youtube.com/watch?v=tf0VtYrbhkQ , both the parents and many of the younger guests at the wedding hold decorated brooms and "sweep out the kallah and chatan ".
In another version, the parents (or just the mother) of the kallah and/or chatan wear crowns of flowers on their heads (hence the second name for this dance, the Krenzl Tanz). In this version, the parents sit in the middle of a circle of wedding guests who dance around them. These guests may hold decorated brooms as they dance by and/or they may give the mother of the kallah/chatan a kiss as they dance by.
Think about adding this minhag when planning your wedding. Mazal Tov!
** For a short explanation of both terms http://www.jewishweddingnetwork.com/jewish-wedding-traditions/birkat-hamazon For the texts: http://pathways.aish.com/pathways/jewishlaw/dailyliving/shevabrachot.pdf