Symbolism, Imagery, Allegory
Brooms aren't just for sweeping. In Boori Ma's hands, the broom is a weapon: "with a few slaps of her broom," Boori Ma can "rout any suspicious character who strayed into the area in order to spit, urinate, or cause some other trouble" (ARD 13). The broom, like Boori Ma herself, is useful because it's versatile, like a Swiss army knife.
The broom is also what people in the land of English lit call a metonym: the broom stands in for Boori Ma because it's so deeply associated with Boori Ma, like the way a pen (or a computer) stands in for a wrier. Note, by the way, that the broom is the one thing Boori Ma keeps when she's thrown out of the building at the end (ARD 76).
Unfortunately, the broom, like Boori Ma, probably won't do a lot of good anywhere else. It is, after all, just "a bundle of reeds" (ARD 76), easily replaced and probably not all that appropriate for a "real durwan" (ARD 74).