This was an old tradition during the American slave culture. In the days when marriages weren't practiced between black couples, the slaves ingeniously created their own cultural solution. When a man and woman decided to marry, they had to jump over a broom held in a vertical position. Jumping over it symbolized entering a new era, which they promised to share together.
Jumping the broom means to take a leap of faith. This was a wedding tradition that was done at most Gypsy weddings originally or Hungarian/European weddings. It was said that it was good luck to jump the broom and take a leap of faith.