"Jumping the broom" is an informal marriage or "partnership." It comes from peasant or gypsy marriages before the idea of a "civil marriage" (going before a justice of the peace to vow marriage oaths) came about in Britain with the Marriage Act 1836 - as an
alternative to a church marriage.
The concept started in France as <i>mariage sur le croix d'un epee</i> ("marriage
on the cross of a sword") which a maudit anglais (Englishman) translated from a French book as "leaping over a broomstick." The original concept comes from ancient military weddings - when a soldier marries one of the women who hung around soldiers
back in the day:
"A sword being laid down
on the ground, the parties to be married joined hands, when the corporal or serjeant of the, company repeated these words: <b>Leap rogue, and jump whore, And then you are married for evermore.</b> Whereupon the happy couple jumped hand in hand over the sword, the drum beating a ruffle; and the parties were ever after considered as man and wife."
My old Cajun stepdad took me aside after I brought the girl I just proposed marriage to home to meet him and Mama, and asked "You can't just go jump the broom?", so I'm here to tell you this expression is for real and old farts like him were still using it.