Modern witches have been jumping brooms at weddings pretty much since there were modern witches. One readily sees why: of the affinity between witches and brooms, you don't need me to tell you.
Jumping the broom in the sense of a de facto marriage, unsanctioned by either church or state, originates in Lalland Scots lore. It's from there that the custom spread to the southeastern US and became current among enslaved Africans, denied the right to legal marriage.
The first time that I presided at a public handfasting, the couple had made for the purpose, from the three traditional woods, a beautiful ritual broom. (Ash, birch, and willow, in case you're wondering.) Lo and behold, come the day of the wedding, the ritual broom languished forgotten at home. (It's not a real ritual unless something goes wrong.) So they ended up jumping a manky old broom from the janitor's closet instead. The broom-jump retained its magical transformative power, nonetheless. Hey, a broom's a broom.
As to meaning, I'll leave that to you to divine. Personally, I can't help but suspect that “jumping the broom” was originally some sort of sexual euphemism, but maybe that's just me. As a humble domestic tool, of course, the broom represents the home and home-life; I've also heard it said to stand-in for the threshold.
In lots of places, couples tend to do a simple run-and-jump—over and off—but around here we do things a little differently. First you sweep the bad luck away from the couple: three times around, widdershins, of course.
Then you lay down the broom. Three times, as people clap, the couple circles deosil, hand-in-hand. Each time around, they jump the broom. Third time over, we pelt them with barley, and done's done.
(Rice? Rice? Ha! What are you, some kind of cowan?)
One jump, or three? Well, it's your handfasting.
Still, you know what they say about third times.
For AE and MF
Many years!