The broom has always signified the domestic side of life. Witches are associated with brooms because their “magic” was thought to be practiced close to the hearth fire. Most “witches” (at least of the Northern European variety) were healers or weavers or spinners. (NB: the “witch children” currently being killed in Africa are often children who have no visible means of support. Brand them as witches, drive them out or kill them, and no one needs to be financially responsible for them.)
So couples who are entering domesticity can symbolize this by jumping the broom.
Tip: This is a nice way to stop and consider what you’re really doing as you marry. It’s not the wedding that’s important. it’s the marriage you’re creating.